I'd start by looking for problems with the switch panel that controls the seat.

I'm not sure what the earlier 124 seat control configuration looks like, but my '94 E320t has a couple of preset buttons that I suppose would override the manual buttons and could cause the manual buttons to appear to be inoperative if the seat was doing a preset thing.

The fact that it begins under acceleration could indicate a loose wire or contact touching a body ground or some other wire.

__________________
Robert Fini

'12 ML350 BlueTec, 100k
'06 E320CDI (x2)
'05 T1N Sprinter 2500/Pleasure-Way Plateau TS, 70k
'97 C36AMG, 319k (son's)
'94 E320T, 249k
'93 190E Sportline LE, 168k (daughter's)
'84 190E-2.3/5spd (Stage Rally Racer)
'66 230 W110 Sedan (Barn Find, Vintage Racer build in progress)