Go to Black Bone Foreat in Big Valley right below where the Trapper is there's a group of wild boars but also a bush where cougars spawn and try to attack you whether on horseback or foot however it works better on foot just make sure you're able to get on a rock in order to avoid being mauled

Fo you usually have a specific time or no

Usually no but for best results try either morning around 8am or either dawn around 6-8pm it has been known to work mid day as well it just depends if you're traveling downwards from where Proghorn Ranch is located it'll have a higher chance than heading towards

Okay thank you. No cougars yet but I did kill a big ol grizzly

Outside of the occasional Grizzly beware of wolf packs

Okay cool

If you need you can set up camp since there aren't any nearby towns besides Strawberry to have multiple attempts at getting the cougar to spawn

I figured as much