invibrake

As said it is supposed to charge the battery with parking lights on the rig, but I found mine needed a 12v line feed to keep the toad fully charged.

The only way I can see the battery being charged is through the taillight circuit back feeding through the power cable into the toad. This would be very minimal charge if any at all.

If your parking lights are on, YES, it does charge the toad battery (up to 2 amps).

Have driven cross country with the Invisibrake without depleting battery.

Guess if you are in nothing but stop and go traffic, brake use could exceed charge rate.

From the Roadmaster Invisibrake manual:
Specifications

Controller Size — 8¾" x 8¾" x 2¾"
Voltage — 12 volts DC
Fuse size — 20 amp
Operating temperature range —
-2° to +150° F (-19° to +66° C)
Maximum amperage draw — 10.8 amps
Idle amperage draw — 6mA
Battery recharging rate — up to 2 amps
Approximate maximum air pressure — 100 psi

No, you must charge the toad battery via running toad or run a charge circuit from MH. It should last a couple days without having to charge toad battery