Vintage Thunderbird Club International

If it's a reddish brown in colour, it could be accumulated varnish from evaporated gasoline. My other (non-Ford) car had this and it clogged the sock filter in the tank. I washed the tank out with detergent and water, then rinsed with methyl hydrate, no problem since.

Hopefully spring assists are included. Not sure about a '57, but on my '56 put a portly mother-in-law and a full tank of gas on board and I might be dragging tail!!

also check the heat riser on the right manifold, should be fully open and holding tight at operating temp.

It's an AGM inside a retro looking case. This one lasted 10 years in my Caddy.

White smoke in the exhaust could certainly be coolant, but the plug usually gets fouled as well. How do they look?

Rough idle and loss of power brakes at the same time could be due to a loss of/leaky vacuum. Be sure to check your booster to engine connections/hose again and see if the booster can hold a vacuum with a hand held pump.

I've used a spray contact cleaner in the past. But in this age of environmental awareness, I'm not sure the new versions would be as effective as the old 'freon' spray I used.
If you go to LED, be sure they are dimmable. I assume dash board bulbs would be, but who knows what comes out of China.

It may be the alignment. Hard acceleration shifts the weight to the rear axle which is on a slightly different trajectory than the front, then on deceleration, the weight shifts back.
Have someone follow you and see if your car crab-walks.

These batteries have a smaller AGM inside a retro looking case. Keep it on a maintainer when the car is parked/winter stored and it will last many years.

Thanks for the photos ... I heard of this, but never actually saw it. On another forum, there's been concerns voiced over inadequate lubrication of the Y-block valve train and this was one of the suggested old school solutions. As 57birdman stated, with the use of detergent and synthetic oils, this ...

If your goal is to make more trunk space yet still carry a spare, many '55 folks on this forum have swapped the full sized spare tire for one of those later 'space saver' spares.
Hopefully, one of them will chime in with year/model/type info, etc.

So just to help clarify the 'high school science' behind a coolant recovery system. From the factory the coolant in a Bird's rad was intended to sit an inch or two down from the cap. When heated up the coolant expands, as every material does, and pressure builds to a predetermined level, that of the...

I put a coolant recovery on both my old cars. It was a kit with canister, hose and rad cap. The hose simply attached to the overflow pipe on the rad and you make a bracket to hold the canister. I didn't notice any improvement in running cooler, but my reason for installing these was to prevent the e...

For my reference on values, I use https://www.nadaguides.com/Cars/1957/Ford/Thunderbird

It may be as simple as your engine idle being set a little too low.
I don't have a 57 shop manual, but I'm thinking it should be around 750 - 800 in neutral, 450 in gear.