It might not be applicable to everything they say within eachother's vicinity, but interpreting Karkat as Tavvy (or, at least a projection of what Gamzee thinks Tavvy thinks of him) seems to work for their conversation in Candy 20.
From the start of their argument, Gamzee repeatedly calls Karkat his 'brother', which wouldn't exactly be too inaccurate of a symbolic descriptor for what Tavvy and he have going on (the implication they split from the same body). After this argument ends, Karkat storms out and Jake immediately strolls in with Tavvy.
'You can't get mad at me because I redeemed myself' in regards to Gamzee is a sentiment Tavvy feels he has to abide by in Candy 18. Karkat also brings up Gamzee licking dirt off his feet, which he infact does attempt to do as Karkat says this. Gamzee ends up actually doing this to Vriska in Candy 32 - another character who was being momentarily used as a substitute for Tavvy.
Whether these are Tavvy's actual thoughts or what Gamzee believes Tavvy feels towards him (or will eventually) is another question... Obviously not literally Tavvy's thoughts at the time present as he's a toddler then but moreso as a ghost haunting him. Regardless the important part is that Gamzee definitely knows that Tavvy really fucking hates him.
Another moment where Gamzee interacts with Karkat, or attempts to do so. Since it's Candy 32 this can either be read as literal or symbolic. If we're thinking of Gamzee doing this of his own volition then he either hates himself for having sex with Vriska or would hate himself for having sex with Tavvy. If we're reading this as Tavvy projecting, then he may believe that Gamzee would hate himself for doing that with him, or that he hates himself for thinking of it. It's vague again but the self-loathing is there.
Also I like how 'hot n heavy horseplay' makes it sound like one of those fake horse costumes with two people in them. The body of two being disguised as the body of one. Hehe
Anyway I can't find much to say on Candy 15, since it's mostly just insults and 'FUCK YOU's but on the topic of Tavvy this line sticks out to me: