will assume this is an ABS car. There were two common ABS systems Chrysler used during this time period and both relied on an electrical pump to provide the boost for the brakes instead of a conventional vacuum assisted brake booster. I think the TC may have used a similar system but not quite the same as the regular Chrysler (Bosch and Bendix) ABS system. The pages here on Allpar point to the TC using a Tevis ABS system. Most likely the pump has failed and will need replaced. That can be very expensive, but probably finding a dealer that can diagnose the system with a scanner is the only way to know for sure. You can remove the ABS system and replace it with a non-ABS system from a car like a 1990+ LeBaron, though it requires a lot of work and even changing the brake pedal assembly.
The DRB II or the DRB III with Supercard can be used to access ABS fault codes. This and a pump pressure test would be the most drect and accurate way of diagnosis.
Is the ABS or BRAKE warning light on?
Yes, it is an ABS system, and both the brake and ABS lights are on.
It has a softball sized black metal ball which I am assuming is the booster, that
has a stem which appears to go down into the bottom of the MC.
well, this stem is quite loose at this entry point. Could I be losing vaccum or pump pressure at this point?
ABS uses a pump, not a vacuum servo, to provide assist. The brake light on non-ABS cars is only activated by a failure in the hydraulic system. Most of the time it's a switch that sits in the middle of a piston that senses pressure in the split diagonal system. A failure in one circuit will push the piston to one side due to unequal pressure, triggering the brake warning light. This light only triggers in a failure mode that impedes operation of the hydraulic system. I think you have a hydraulic failure that's causing the ABS failure, possibly in the master cylinder. Both lights on do mean that it's not an electronic failure though. These systems are unreliable, as mentioned before, and it might be worth swapping in a non-ABS system, especially to keep another one of these unusual cars on the road.
The TC ( all TC's, the "Q" body ) use a Teves anti lock brake system that is unique to the TC but is similar to the Teves systems used on other European cars ( and possibly the Buick Grand Nationals)
The black sphere is the high pressure accumulator and the post that it's mounted on shouldn't be loose. These accumulators have an internal bladder and these are known to fail with age. Normally these are charged with very high pressure by the system pump.
You'll want to check the large fuse ( 30 Amp ? ) in the brake system fuse block which is on the passenger side inner fender near the air conditioner's receiver/dryer. The fuse supplies the ABS boost motor and these terminals and the attached wiring are known to corrode and fail. You'll want to look at the terminals carefully including the underside.
You'll want to consult the service manual for any of the three years of the TC and in addition, you'll want to reach out and join the only national club that's devoted specifically to the TC's: TC America. You can go to their website for more info: www.chryslertcbymaseraticlub.com There have been numerous ( more than a dozen ) articles published in the TC America newsletter regarding the care, maintainence and repairs to the Teves system. I'm sure you'll be able to purchase those issues of the newletter that pertain to the system.
The rest of the brake system is based on the components of the 4 wheel disc setup of the 1988 Dodge Daytona ( G body ).