When should you apply for a 30-day extension at local immigration in Thailand?

Yes do it early, I’ve made the mistake of leaving it to the last minute, and I’ve ended up in a position where I might have to go home.

Usually within 30 days. You don't lose any days, it's added to your existing stay

You should go as early as you can, and not wait until the last minute. The time will be added onto the end of your stay, so you don't lose any time by going early.

At most immigration offices you can apply for a tourist extension when you have 30 days or less left on your existing stamp.

At some immigration offices you can apply when you have 45 days or less left (Bangkok, Phuket, Chiang Mai, a couple more)

And at a few you can only apply during the last week, or even less (Pattaya, Koh Samui, Koh Phangan)

You're able to apply up until the date on the stamp in your passport.

When I've done it before I go about 2 weeks before the 60 day is up