My 2004 Maurader does a series of slight pauses when idiling or coming to a stop. Has 39K miles.The dealer cant find anything wrong ?

What do you mean by pauses? If the idle is irregular you might want to install a new idle control valve.

It does a slight hesitation. Like a little rumble?

Could it be my gas. I use premium. I have it down to a quarter of a tank. Should I add some additive ?

It would not hurt to add some fuel injector cleaner. I think Techron is the best.

Just so you know my truck which uses a similar engine to your car had a problem with the IAC valve. Techron would smooth it out temporarily but once I replaced the valve it idled like new. The cost is not high so you are not wasting much if you replace it. Dealer costs will be higher than independent shops.