Without actually checking I would suspect that there is NO unlicenced radio that is actually ALLOWED to transmit continuously - such transmissions usually require licencing. I suspect that continuous transmission is referred to as broadcasting which is a different thing and usually under much more strict regulation.
There's no reason you couldn't use a timer to 'key' a transmitter (CB, whatever) for as long as you're allowed but, then again, keying without modulation is another legally dodgy thing.
If we knew more about what you wanted to achieve (and why) we might be able to advise further - for example, do you need 'range' to do your test (very low powered transmitters often fall outside legal rulings so you could achieve your result using something like that)?