Generally I c-bet with a polarized range. This means I'll c-bet the following:

TPGK+
Some draws, usually the ones that don't have any showdown value
Air with backdoor draws or some sort of ability to beat villain's continuing range

And then I'll check the following:

The occasional slowplay
TPWK
2nd/3rd pair
Some draws, usually the ones with some sort of showdown value
Other air

My question is: When should I cbet 2nd/3rd pair? I imagine that 2nd and 3rd pair would play a mixed strategy at equilibrium, since being able to have trips when the middle or low card on the board pairs up is useful. My guess is that 2nd and 3rd pair do more checking than betting, but that they would cbet at like a frequency of 20%. Since I'll arrive to the flop with a variety of 2nd and 3rd pair holdings, if I were to not to play any of them with a mixed strategy, that is, I'd play each one using a pure strategy but use a mixed strategy for my entire range of 2nd and 3rd pairs, which ones should I choose to cbet with rather than check? Also are there any situations where I would want to bet most of them at a high frequency? Here's what I'm thinking so far:

2nd pair + good kicker is better to bet than 2nd pair + weak kicker.

The more overcards there are to the middle card on the board, the more important it is to cbet 2nd pair for the sake of protection. I think this could be extended to draw heavy boards, but avoiding a raise may be prudent.

The higher the middle card is the more value we can expect from cbetting 2nd pair with a good kicker. This is because people will play more hands preflop containing higher cards, so we can expect to get called by more worse middle pairs. Of course we also need less protection when the middle card is higher, so these two factors work against each other.

If our range is very air heavy, then betting 2nd/3rd pair lets us bluff more. Of course if we're cbetting with a high frequency then we usually want to use a smaller sizing so that our opponent is forced to continue with worse, but if we use a smaller sizing we can't bluff as much...