That's promising then, because a fault with the head itself would tend not to be intermittent. I'm sure I read somewhere that these lovely big old things are prone to dirty switches (as is almost any device that's been around for a decade or three) and certainly that would also cause erratic behaviour but what confounds that theory in this case is that it only does this on tape, but possibly - and I've met this issue on a Hacker RPC1's Nakamichi-built cassette deck - the leadout from the head is flexing (as it will when the heads move to make contact with the tape) and pulling away at a part-thickness fracture of a connection. Most likely the core as the braid is typically softer and thicker, but could also be caused by the constant movement over the years causing the braid to wear away at the insulation on the right channel core wire from the head, causing an intermittent short. The reason it remains functional when the tape is playing being that such a fault in that wire would only manifest itself when the head moves at the start or the end of play.