I'm trying to recall a sketch - thought it was Tommy Cooper but maybe not. It involved a guitar or ukelele where the fretboard was attached in reverse to the body.

Does anyone know it?

Do you mean the back of the neck of the guitar as opposed to the front?
I'm not sure why I'm even asking because I have no idea, but it rings a bell.

Actually on second thoughts there is no bell ringing. It dinged once upon first reading but now that bell hangs flaccid, swaying sadly in the cold, depressing breeze of its own failure.

RUSS ABBOTT! Was it Russ Abbott? See, even now I'm doubting myself.

Dunno.

Yes - I guess that's what I mean - don't know much about musical instruments. The comedian made a big thing of picking up this ukelele (?) and finding he could strum but the strings didn't go all the way to the end. Instead, the strings for fingering were on the back of the fretboard etc. etc