Confessing after you’re caught is still honesty. It’s just honesty on clearance.

Timing changes what an admission is worth. Owning it once the evidence is out is still better than denying it, and it buys much less, because the other person now knows you were content to let it stand while you could. The truth turned up just after its value dropped. That does not make it worthless, only discounted.

If you are sitting on something, say it before circumstances say it for you. If you have already been caught, admit the whole of it rather than the part that was found. Then expect to rebuild slowly and do not argue about the price.