The male genitalia (penis) when in contact by any means of the female genitalia (vagina).
'Tabby wacker': 'wacker' perhaps meaning the 'penis', and 'tabby' an alternative word for 'vagina' and perhaps from 'pussy(cat/tabby cat)' (?)
I had never heard of this before. Apparently, and quoting an internet forum user, "The Bard (Scottish poet Robert Burns) used the phrase regularly". Is it then a Scottish term?
I don't think Robert Burns used it in his poetry, but I could be wrong.
The poster I spotted using it on an internet forum wrote it as one whole word. I happen to think it is two words, largely to take account of the male and female genitalia separately. It could perhaps be hyphenated (?)
"I used my tabbywacker last night after a drunken night out."