On the fifth day of Gil, when the map option comes out, don’t go to the playground, go directly home, and then you will meet Mark. After that do "feel awful" and pick up the phone after that go to playground and tell gil you like him and "admit". Finally when gil comes at your house , choose “Make a joke” when talking to him and enjoy the touchy ending.
Okay I'm sorry but that did not help me either because on day five I chose to go directly home you meet mark on day 5 and then later on he calls you and you choose to hang out with him or go straight to bed going straight to bed just ends day 5 and day 6 never happens choosing to go to the playground with him gets him to come home with you but nothing happens and there was never a make a joke option in the playthrough this Choice also ends day 5 with day Six never happening. I tried playing around with your hint though to see if I could get it to happen but on other playthroughs never did I ever find a make a joke option.
I decided to play the route again,I did the touchy ending a while ago and got some things wrong first I forgot there was no day 6 ,so I'm going to be more precise about the choices you have to make. On day five don't go to the playground just go home ,you will meet mark after that choose to feel awful after that pick up the phone and go to playground with gil then say you like him and admit after that you will come back home and then you can make a joke and you will get the touchy ending.