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My method is to skip time to dawn, speed it up until either the Travelling Merchant spawns or until it is 1:00 PM, then skip to midnight, then skip to dawn again and repeat the cycle. But you need to alternate between dawn and midnight; if you only skip to dawn then you stay on the same day and the Travelling Merchant will never spawn.
If you are not in Journey Mode then you should be able to use a bed to advance time. It is slower and you can't skip ahead but it is still faster than letting time go by on its own.
If you are really desperate (and I can understand that - RNG can be a pain in the arse sometimes) then you can either download tEdit and force-spawn the Travelling Merchant or download the Builder's Workshop from Curseforge and look for whatever you want to buy from the Travelling Merchant NPC there. But this should only ever be a last resort when you feel like waiting for the Travelling Merchant is ruining your gameplay.
That 22% chance is somewhere between 1 out of 5 and 1 out of 4 every *day* that the Travelling Merchant will spawn. It is less than 50% so it is more likely than not he won't spawn but if you speed up time you don't need to wait as long between each dice role. That was why I suggested either using Journey Mode or sleeping through the rest of the day and night.