Yes there's a Clock battery for the TT... 4.5VDC iirc, bought some Mac 4.5VDC PRAM batteries to try, though I haven't yet because they're 2 wire and as I recall the TT's clock battery is 3 or 4... and they'd be simple to replace with the right one... just a simple plug affair.
Also, the TT's Clock was notoriously innacurate, though never saw one as bad as yours.