If you have a wiring diagram and electrical tester you could test the dash switch in detail.

Or you might just swap in another switch from a junker or a friend's 240 to see if that fixes things. I wouldn't spend the money on a new part on speculation.

Some background information -

The Ign. Switch positions are 0, I, II, III (start)

Due to the design of the main headlight relay system (completely separate from the high beam/low beam "step relay") on '86 and later 240s, the dash switch's input lead for the "headlight" position only receives power at ign. position I and II. Possibly that wire or terminal is shorting to the switch's parking light output.

That scenarion would give the parking lights coming on when in posiiton I and II regardless of where you set the switch.

If not that then I'd suspect some wires were switched around on the fuse panel or elsewhere.

--
DAMHIK: Don't Ask Me How I Know - - - Sven: '89 245, IPD sways, electric rad. fan conversion, e-codes, 28+ mpg - auto tranny. 500 mi/week commute. '89 245 #2 (wifemobile). '90 244 (spare, runs).