Instead of putting a dead short on the cable, one could use a resistor. Then you could identify between an open cable, a shorted cable, or a cable that has the correct resistance on it and is therefore intact and the one you want.
You could use a 75-ohm terminating resistor for this. It's already packaged in an F connector, so you could just use an F81 splice barrel and connect it straight to the cable you want to test.
In a lot of cable systems, you don't really even need a TV. Just use an FM radio (not a digital one, just a cheap analog tuning model with an antenna). Even if the cable system isn't rebroadcasting any FM stations (most aren't anymore), there are several cable TV channels with their audio in the FM band:
95 has it's audio at 95.75MHz
96 has it's audio at 101.75MHz
97 has it's audio at 107.75MHz
You could also use a radio scanner. I've used a scanner to identify cable signal leaks...just tune it to an audio carrier in the range that the radio can tune and then bring it's antenna near your cables. Should you start hearing the TV audio, you have a signal leak.
Here is a list of all the cable channel frequencies. Note that you must add 4.5MHz to the visual carrier to get the audio carrier:http://www.jneuhaus.com/fccindex/cablech.html
Another way to check for signal, the cheapest way I can think of:
Since the video carriers are AM one could build a simple crystal-set style detector circuit in conjunction with a high-impedance amplifier or earphone. I expect this will emit a strong 60Hz tone (the vertical sync) when connected to an active cable line. This can be done with nothing more than a diode.
Several years ago when I used a cassette-tape adapter to feed my car stereo the input from my mp3 player, it did a fine job of picking up the video carrier's vertical sync and blasting the 60Hz tone through my car stereo speakers anytime I drove by a TV transmitter tower.
So I believe a simple detector circuit will work just fine for the purposes of checking for signal on a cable TV line.