Is there any means for a character to pretend to be subject to a mind-effecting spell or ability after resisting or being immune, so as not to alert the caster?
There's a spell that does exactly this from Complete Scoundrel, called Disobedience. It's 3rd level (bard, sorcerer, wizard, spellthief) lasts 1 hour/level, and suppresses any spell that grants mental control. Anyone using such an ability has to make a will save or think the effect worked, and you still get to receive the orders so you can fake being controlled
Not if it was targeted: the caster can sense you succeeded
The core rules state under Saving Throws/Succeeding on a Saving Throw
A creature that successfully saves against a spell that has no obvious physical effects feels a hostile force or a tingle, but cannot deduce the exact nature of the attack. Likewise, if a creature’s saving throw succeeds against a targeted spell you sense that the spell has failed. You do not sense when creatures succeed on saves against effect and area spells.
Most mind affecting spells target a single creature (for example Charm Person and Dominate Person target a single humanoid, Suggestion one living creature). Enthrall targets any number of creatures. Because these spells target the creatures, the caster can sense that the spell has failed, and any pretense to the opposite is not going to bluff them.
However, you can fake being affected by a spell like hypnotic pattern, because that is an area spell, and thus not subject to the caster sensing the spell has failed. How to resolve this is up to the DM -- either through roleplay, or most likely, using a bluff check against the caster's sense motive.
Likewise, there is no explict rule that says the caster senses it if the spell fails due to immunity, so if you are immune, you probably could also bluff (although the DM might of course rule otherwise).
Lastly @StevenTG found a spell that allows you to specifically override this behaviour, Disobedience (available to Bards, Sorcerers, Wizards and Spellthieves at spell level 3):
In addition to protecting the subject, disobedience sends false information to the creature that is attempting to gain control of the subject. The would-be controller must succeed on a Will save or believe that its spell or ability has taken effect and that the target is now under its control. The spell's subject becomes aware of commands issued by that creature and can choose to act however she pleases, disregarding the would-be controller's orders or going along with them in a pretense of obedience.
If you have such a caster in your group, that is a good way to pull it off.
A bluff check opposed by the caster's sense motive check is the best way. The DM would add a modifier based on whatever they thought was appropriate.
The DM might choose to use the casters spellcraft or knowledge: arcana, too, since they might be more realistic/favorable to the caster.
Note that, even for a single target spell, bluff is still appropriate. It won't be easy, though:
The bluff is way out there, almost too incredible to consider. +20 [bonus to opposed roll]
Note that someone sensing that the target succeeded their saving throw is not the same as knowing a target succeededed their saving throw. Even if it were, a character with high bluff can very well convince a less-skilled opponent that something that person witnessed first-hand was something else entirely, at least for a time. Bluff is powerful, so it is up to the DM to regulate much as they do with allowing researched spells or new magic items.