This is a tricky problem, but the detailed troubleshooting you've already done is excellent. Here's a breakdown of possible causes and additional troubleshooting steps based on your observations

Summary of Key Observations and What They Suggest:
Load Sensitivity

The dimming is happening with the vacuum cleaner (a motor load) but not with a similar resistive load from a heat blanket, even if the voltage dip is comparable. This strongly suggests a problem related to the type of load. Motors draw a lot of current when they start and their current draw can fluctuate while running (especially if the vacuum is on carpet, then hardwood, etc).

Specific Fixtures

The fact that some LED fixtures dim while others (even on the same circuit) don't, and that incandescent/CFL bulbs dim similarly, points away from the LED fixtures/bulbs themselves being the primary issue. It suggests some fixtures are more sensitive to fluctuations than others.

Voltage Dip

The voltage dip is significant (121V to 104V), indicating a substantial voltage drop under load. This could be from inadequate wiring (size or connection), a poor neutral, or other issues on the line.

Table Lamp Test

The table lamp dimming in some circuits and not in others is VERY informative. It suggests specific circuits within the house are more susceptible to the voltage fluctuations caused by the vacuum.

Utility Check

The utility's claim of no problems should be verified, but you need to consider the rest of your diagnostic tools.

Possible Causes & Troubleshooting Steps


Neutral Issues (High Priority)



Load on Neutral

Even though the utility claims the neutral is good, inside the house is where the majority of the problem seems to stem from.

Voltage Drop

The voltage dip you are observing indicates a problem.

Multi-wire Branch Circuits (MWBCs)

If you have MWBCs, a shared neutral carrying too much current can cause voltage imbalances and dimming on one phase.

Test

With all circuits off, measure the resistance between the neutral bus in each panel and a known good ground (cold water pipe). A high resistance indicates a loose or corroded neutral connection.

Check for Current on Neutral

Measure the current on the neutral wire going to each panel with the vacuum cleaner running. A high current on the neutral could indicate a problem with unbalanced loads or a neutral connection.2.

Shared Circuit with Motor



Dedicated Circuit

Put the vacuum on a dedicated circuit. This would at least keep it from interfering with the lights. It also gives you the option to add an isolation transformer to the vacuum cleaner.

Plug-in Motor Filter

An online search will provide you with filters you can plug in between the vacuum cleaner and the wall.3.

Branch Circuit Impedance (High Resistance Wires)



Impedance

The fact that some table lamp locations dim and others don't strongly points to this. The circuits that dim are likely to have higher impedance in the wire from the panel to the receptacle. This could be from a long wire run, undersized wiring, or bad connections.

Wire Size

Double-check the wire gauge used for the circuits that are experiencing dimming. Are they undersized for the length of the run?

Connection Issues

Every connection on the circuit needs to be checked. Look for: Loose screw terminals at receptacles, switches, and in the panel. Poor wire nut connections (corroded, loose, too many wires). Back-stabbed receptacles (these are notorious for poor connections). Replace them with receptacles that use screw terminals.4.

Panel Connections (Also High Priority)



Bus Bar Connection

Verify that the breakers are making solid contact with the bus bars in the panels. Look for corrosion or signs of overheating. Tighten breaker connections if possible (while power is OFF!).

Main Feed Lugs

Check the tightness of the main feed lugs where the service entrance conductors connect to the main breaker. Loose connections can cause voltage drops.

Neutral/Ground Bus

Make sure the neutral and ground bus bars are properly bonded to the panel enclosure.5.

Generator/Transfer Switch Issues



Bypass the Generator System

If possible, temporarily bypass the transfer switches and power the house directly from the utility to see if the problem disappears. This would isolate the generator/transfer switch system.

Transfer Switch Contacts

Inspect the transfer switch contacts for signs of burning or corrosion. Clean them if necessary.6.

Specific Fixture Sensitivity

You've already started down this path with the keyless. Some fixtures, especially those with electronic drivers (LEDs), can be more sensitive to voltage fluctuations than others.

Detailed Troubleshooting Steps



Voltage Drop Testing (Most Important)



Under Load

With the vacuum running, measure the voltage at the panel, at the receptacle where the vacuum is plugged in, and at the dimming lights. This will pinpoint where the voltage drop is occurring. Measure phase to neutral, phase to ground, and neutral to ground. A significant voltage difference between these points indicates a wiring problem.

Voltage Sag Study

Use a recording voltmeter/power quality analyzer to monitor the voltage over time. This can capture voltage sags/dips that are happening too quickly to see with a standard voltmeter. This can also help you identify the exact characteristics of the voltage fluctuations caused by the vacuum.

Circuit Isolation



One Circuit at a Time

Turn off all breakers except for the one circuit with the dimming lights and the receptacle where the vacuum is plugged in. Does the dimming still occur? If so, the problem is likely isolated to that circuit. If not, turn on additional circuits one at a time until the dimming reappears to narrow down the issue.

Extension Cord Test



Powering Fixture Directly

Your plan to power a dimming fixture directly with an extension cord from a known good circuit is a good one. Make sure the extension cord is heavy-duty (12 gauge or better) to minimize voltage drop in the cord itself.

Bypass House Wiring

Your plan of bypassing the in-house wiring using the extension cord will test to see if the problem persists. If so, then the problem is from the utility and you are stuck telling the client that the utility has to fix it.

Recommendations for Specific Action


Focus on Neutral Connections and Wiring Impedance

This is the most likely culprit. Methodically check every connection from the panel to the affected fixtures and receptacles.2.

Voltage Drop Testing is Crucial

Do detailed voltage drop testing under load to pinpoint the location of the voltage drop.3.

Simplify and Isolate

Keep simplifying the circuit (one circuit at a time) until the problem is isolated.4.

Document Everything

Keep detailed notes of all your measurements and changes. This will help you track your progress and identify patterns.5.

Consult a Power Quality Expert: If you're still stumped after trying these steps, consider consulting a power quality expert. They have specialized equipment and knowledge to diagnose complex electrical problems.Good luck! This sounds like a frustrating problem, but your methodical approach should eventually lead to a solution. Flag for review