I have no experience with BJ, having only watched them on TV, but here are some thoughts anyway:
Assuming all of BJ's listings are still No Reserve, I can't think of a reason an appraisal would be needed. But if you do need/want one, you could appraise it yourself pretty easily by checking Bring a Trailer's prior GT listings:
https://bringatrailer.com/ford/gt/ ... just find the most recent listings that have
1) similar mileage,
2) same stripes (ie the optional Full Stripes (the double over-the-top stripes and side stripes), Side Stripes Only, or Stripe Delete (no stripes top or sides, and the window sticker actually states "BODY SIDE TAPE STRIPE DELETE" otherwise the side stripes were just peeled off) and the
3) same color, as these 3 details seem to be the most important to buyers.
Again, I don't have any experience with BJ but do know their fees to the Seller (8% of hammer) and Buyer (10%) are much, much higher than Bring a Trailer's. In case you're not aware Bring a Trailer charges (
https://bringatrailer.com/how-bat-works/#seller-fees) a $99 listing fee plus $330 for pics unless you want to take care of them yourself, and the buyer pays 5% capped at $7,500 ... so Bring a Trailer would net under $8,000 from a $400,000 sale, while BJ would net $72,000. Hopefully their higher fees are worth it.
As for your tune-up question, I feel like no matter where you sell it a full service (tires, belts, hoses, fluids, brake pads, A/C check/recharge, alignment, etc) probably always helps on a GT with more than about 500 miles on the ODO, whereas with mileage under that the car may be destined for a museum / collection with no intentions of ever driving it and those buyers might prefer every single detail is OEM as it left the factory including tires, belts, filters, all delivery items such as windshield decals / seat covers / steering wheel cover / steering wheel center cap cover / floor mat covers / hanging warning tags, etc.
As for your question re specific things buyers want to see or want original, I would want/expect, in order of importance to me: Both keys/fobs, the OEM car cover in its OEM bag, the OEM floor mats, the OEM tire inflator/tow hook, the original window sticker, the owner's manual in its case, the delivery items I mentioned above, as much documentation as possible including original sales docs and any subsequent sales docs, all maintenance docs, all repair docs, anything and everything that documents the car's history ... and make sure every square inch including the bottom, wheels, wheel wells, door jambs, frunk, engine bay, etc are very clean.
Good luck!
