This sounds exactly like a typical problem in the later 240s.

On the '93s, there's a relay in the center of the dash deep behind the center vents (the ones under the radio). The problem isn't really the relay, but the relay's plug (or connector if you want to call it that). Because of the stupid way these later model year 240s were wired (the older cars kept most of the heavy wiring in the engine compartment, including this relay), there's a lot of current flowing through these plugs inside the dash, and they sort of melt and short.

Art Bernstein, as I recall, has an interesting set of pictures of this problem, which is typical of these last 240s. You have to change the relay, and also the connector (which you'll find is burned or scorched). The fun is getting to the relay -- you can't get to it from the side (glove box) like you can the OD relay.

As one who put high-wattage H4 bulbs in his car (with Cibie/Volvo Euroheadlights, of course), a priority was to use the relay method of wiring it so that only a trickle of current actually goes through the car's original wiring, including that relay in the dash.

You don't need to have installed high wattage bulbs, however, to suffer this problem -- it's just that high wattage bulbs will exacerbate the problem and make it more likely.