Unless the boat was wet sanded many times it would be rare and hard to believe the gelcoat is thin unless it was a repair area. Boat yards are in the business of painting boats and make far more money in labor with a new paint job then they do with a buff & puff.
Gelcoat is quite thick when compared to paint and can be buffed lots before wearing it away. Most any gelcoat can be restored and it will cost about 9k less than a paint job.
As was stated Poli-Glow is another option but it is an acrylic coating that does not like fender rash or mooring balls rubbing on it. This is a good option if it is indeed thin. I have a 30 year old boat and even the decks, which get the most UV abuse, are still plenty thick.
Re-conditioned this one last week with a couple of friends...
9:00 am:

9:30 am:

Working down the cove stripe Before/After:

The toughest reflection is always straight on:

The detail in the reflection tells when it's shiny enough to start waxing:

My shoulders still hurt..
She came out amazingly well for a 1987 that was fairly chalky! Actually she looks like she was recently painted..
That's my buddy Tim on the ladder. I am once agian going to make the shamelss plug for Presta Products. I can honestly say that I have no future use for any compounds or polishes other than Presta. My buffing and polishing directions just got a LOT easier.
To say this stuff is amazing at what it does, & does not do for that matter, no "essential oils" or silicones & no swirl marks, would be an understatement.
If a boat is heavily oxidize/chalky the Presta Gel Coat Compound starts at a P800 level & then does amazing things. It finishes with a shine that is not all that far off of Finesse It II and a finish that would not be discernible from Finesse It II to 98% of boaters. These products use a technology called "diminishing grit" which allows the grit to start at a P800 and finish at a level that can be double that or more as it breaks down to smaller particle sizes during use. Based on the shine left with the Gelcoat Compound I'd say that it was finishing at between P1600 & P1800.
Presta Gelcoat Compound (LINK)
ThePresta Ultra Cutting Creme starts a little higher, about P1200 level yet clearly finishes off at a VERY, VERY high level of shine equal or better than that of Finesse It II..
Presta Ultra Cutting Creme (LINK)
I would also like to shamelessly plug the Makita 9227C buffers we used. We had three of them on site that day and not a one of them gave us so much as a hiccup. Mine in particular, and Tim's, have seen some serious use. Our friend Chris made the comment "WOW.... ouch... these things get HOT !!" and this is why you need a machine that can withstand the abuse..
Presta products usually need to be ordered but it is 150% worth every ounce of effort and money you spend.
Actually the prices are better than what you'd pay for lesser quality products at most marine stores.
A 32oz Ultra Cutting Creme is $19.56
A 32oz Gelcoat Compound is $20.92
These are direct from the manufacturer prices so it may cost less if you can find a local Presta distributor.
What we used on this boat:
First Pass = Presta Gelcoat Compound with the Presta 9" black colored wool pad (it is recommended to use the white Presta wool pad with the Gelcoat Compound but we found the black to give higher finish shine. I think Tim was using speeds below the #2 dial setting on the Makita buffer and he was buffing nearly dry but not all the way. One 32oz bottle did the entire Ericson 34.
Second Pass = Presta Ultra Cutting Creme with a 3M Hook It Polishing grade wool pad #05713. This is a neat trick, using a polishing grade pad with a compound. It allows you to have a higher final shine when using a diminishing grit compound than you would using a compound grade pad with the Ultra Cutting Creme diminishing grit product. I was starting at speeds around 2 and finishing off at speeds of about 3.5 - 4 on the Makita buffer. I too was nearly buffing dry but leaving enough wet to not load the pad. (I would not suggest "dry buffing" until you have some experience)
Final Pass = Collinite Fleet Paste Wax #885. Tim's wife applied this with a microfiber foam applicator and a spritz of water from a spray bottle sprayed directly to the hull. It was then wiped and polished up with microfiber rags.