Golden Pigs appear in Campaign and Tower Tournament modes only - they have a high chance of appearing and you will likely only need a few runs to get the daily quota (the current event in August 2022 has 3/day, but sometimes it’s only 1)
Once this pig appears, you need to kill the pig quickly before it escapes (I’m not sure if an escape counts against your quota - I’ve never let that happen) and you need to ensure you clear the room (like almost all other loot, you will only collect it if you clear the room it drops in)
Therefore, if you are playing the tournament at higher floors, switch to campaign mode until you get the pig/s - in a tough run the fire the pig draws away from other enemies (or just generally the distraction) could get you killed
Even in campaign, for the same reasons, don’t play your highest level if you can’t clear it even with shitty perks - drop down a world or maybe even 2. There’s no benefit in dropping too much - you are losing out on XP, coins and general loot
There isn’t really anything you can do to make them more likely to appear (Eg isn’t affected by Equipment Drop Chance nor proc’ed by Jackbot) but they are so easy to find that it doesn’t matter
Also, in the past it was possible to hold on to the tickets and use them at a future event where the prizes on the wheel are better (and you might find suggestions to do that on some Autofire communities) but that was patched a long while back