I think this is from a acoustic duo in the 1990's that had only one album. I tapped it out on my keyboard and the melody of some parts is like this:

DDD DDCBfD DDEEEDCBfA

And another brief hook:

CCGFGAF

My profound apologies to all you real musicians out there! It was the best I could do. Any ideas?

It sounds a little like Bourgeois Tagg's "I Don't Mind at All," although that was from the late '80s.