Yes cars (When towed) can have air brakes.
Mine had electric brakes.. I wish I'd have had an indicator would have saved me several hundred dollars.
There are two types of AIR/Hydraulic brake systems used on cars.
One (M&G as I recall) goes between the brake booster and the brake master cylinder.. This type I'd not expect any issues with nor will the most common indicator work with it.
The other types (There are really two versions of this) either push or pull the pedal, they work the same, the "indicator" is a light hooked to the brake light switch. When thepedal is pushed the light comes on. (Easy isn't it) a very good system I might add.
When they installed it the dealer removed and replaced a plastic panel under the dash.. They put it on shifted to one side. it thus rubbed up against the brake pedal arm and held them on Cost me a full brake job INCLUDING Rotors (OUCH).
I tossed the panel in the trash.
This is just one way to mess up an install. but you need to check it.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times