The speed control on your Town Car requires a signal from your brake pedal position (BPP) switch to verify function so that when you hit the brake pedal, the switch triggers the ABS module which then triggers the Powertrain Control Module (PCM) to shut down the speed control system. This signal wire is a separate wire from the signal wire that tells your lighting control module to turn your brake lights on.
Secondly, there is a speed control deactivation switch mounted right near the brake light switch which is kind of a "safety" sensor that will deactivate your speed control with more the use of more forceful brake pedal operation. This has only two wires on the connector.
Based on all this information, what I would recommend to you is to disconnect that BPP switch you just installed and have a hard look at the wiring connector and wiring. Ensure there are no burned or melted wiring or terminals. This can cause your problem; the connector is often damaged when you find a bad switch. You can purchase the connector by itself, and wire it into the existing harness.
Secondly, verify the plug for the speed control deactivation switch is fully seated, since you were working in that area. It somehow may have become dislodged.