Can only say anecdotally, personal experience only. Around ~10 restarts of game and hence ~10 boar farm setting up and my exp has been -

1- always boar spawn right near new char start loc but never 2 star there, so ignore 1st close spawn imo

2 - seems complete RNG whether 2 stars spawn further away or next island, but plenty of times had 2 star spawn on same 'starter' landmass my new char landed on so imo don't believe suggestions must leave starter island

3 - 2 star spawn is definitely RNG but in my exp, either a site can spawn 1-2 stars or just doesn't. So here is my ABC rule of getting my 2 star (all you need is 1 since breeding normal boar gets 50-50 chance of 2 star piglet)

a) if boar spawn area has only no star boars when you discover it, imo just ignore that site bc I've never had 2 star pop after clearing out those first boar over and over

b) if boar spawn area has 1 star boar then it is possible but no guarantee 2 star will RNG spawn. But good to try, and this is method I use to easily contain any that spawn
b1 - kill the first 1 star and other boar, while waiting for respawn timer, build a pen and catch tunnel (where you lead boar into the pen
b2 - build a workbench right there - this forces no boars to spawn while you are away, but game keeps the respawn timer ticking away
b3 - come back when you think timer is up, boars won't be spawned yet or mistakenly killed, run off etc b/c workbench forces no spawn
b4 - destroy the workbench and if timer on respawn is up, boars will insta spawn at the spawn location. Either 2 star will be there and you catch it, or not - and you easily kill all the boars that just popped

c) run around main starter landmass in meadows looking for more boar spawn areas with at least one 1-star there, and repeat workbench traps above. I just run around to my 3-4 workbench traps whenever feel like checking, and quickly spawn 3-4 sets and see if I get a 2 star

Note - there have been a few game restarts where literally no 2 star boars would spawn on my starter landmass. But mostly, I'd say 70-30, maybe 2of3, I've been able to get a 2 star eventually long as I am checking only locs that had at least a 1-star able to spawn

Repeat - all this is anecdotal. In grand scheme of things, 10 new game restarts is not exactly large sample size to make actual math decisions on. That said, works for me mostly.