"Now having said all that, whenever turn signals create bizarre behaviour in time with the flasher or things change when touching the brake then it’s normally a bad or weak ground or electrical contact at one of the corner lamp assemblies (front or more often the back), but could also be in the bulb sensor. Typically what’s happening is the current passing through a lit bulb isn’t going straight to chassis ground, but is back feeding to ground through another route with a lower resistance, which is often through another bulb such as a brake light or park light, normally at the same assembly, but not always. If that other circuit is on the bulb sensor that can trigger a warning in time with the flash. If the bad ground or contact is simply weak and not broken then the problem may seem intermittent, often related to temperature and humidity. People who own or service trailers know these problems all too well."

Agreed.

The turn signals are not monitored by the bulb failure sensor, as the diagram that Art posted clearly shows. Instead, the clue of a failed turn signal bulb is a doubling of the flashing frequency whenever the side with the failed bulb is selected. I tested this on my 1992 245.

I'm agreeing on the fact that a faulty (as in a somewhat higher resistance) ground return may be the cause of the sensor getting a little upset. If the ground return current of the turn signal doesn't all go cleanly via the normal path, part of it will find its way through other bulb filaments.
That will affect the total current through that other bulb. If that puts it outside the specs the failure sensor is looking for, it will trigger the warning light.
Given the fact that the warning light flashes in sync with the turn signals, is why I think this is likely the case here.
Given the other fact mentioned about it going off whenever the brakes are applied, confirms this for me. The brake lights then present a parallel circuit of lower resistance compared to the running (aka park) lights (21 W vs 5 W).

A clue of a bad return path is if the running lights dim visibly whenever the turn signal is lit. Check for that, it's a pretty common phenomenon on older cars.

In the European setup of a 245, the rear running lights and brake lights are combined in a dual filament 5 W/21 W bulb and the turn signal is on its own single filament 21 W bulb behind the amber lens. And together with the fog and reverse lights, they all share the same return path in the assembly.
Now, I'm not aware if Volvo ever did the North American setup of combined brake/turn signals, but apart from a more convoluted relay setup, it shouldn't make any difference on the warning sensor side.

P.S. If you ever wondered during your school days way back if you were ever going to apply physics in real life, well this is one of such occasions you actually get to find that out. (Ohm's and Kirchoff's Laws, in this case).
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1992 245 Polar B200F M47