Anderslober,
I have a '71 Mach 1 with the 351c, I am not running the advance/retard unit as it originally was equipped with, rather, changed it out for a Non-California Ford distributor which has a single advance used in pre-smog cars. I believe the distributors used in both 351c's and 429/460 engines utilize the same fitting distributor. If you are not opposed to aftermarket parts, Standard Ignition offers a single diaphragm vacuum advance which comes with adjustment instructions to adjust to various Ford distributor numbers, and can be ordered under part number VC-31. Borg-Warner sells the same vacuum advance as part number VC-311, adjustable as well. Over the years I have used both.
The Thermostatic Vacuum Switch with the three nipples is part of the smog package. It's purpose is to withhold vacuum from the distributor vacuum advance until the engine warms up and coolant temp reaches operating temp, when the switch will allow the vacuum to operate the distributor vacuum advance as normal. In this way, cold engines will warm up faster having slightly retarded timing . My shop manual shows where each vac hose goes from the factory. I also have left the switch in place, however I just run a ported vacuum hose from the base of the carb to the single advance distributor. Everything works just fine .