While it seems you're trying to use the stock car antenna to improve your over-the-air television signal, you might be wise to consider installing an additional antenna instead.
While it may be true that the stock antenna can help in picking up a few signals, the antenna is tuned for AM/FM radio usage and will not help with most of the TV channel frequencies. Let me explain:
AM radio (Amplitude Modulated) carrier frequencies are in the 535-1605 kHz frequencies and is considered a fairly low band. FM radio however is smack dab in the middle of the VHF TV chunks. VHF TV channels 2 through 6 are before the FM radio channels, and VHF channels 7 through 13 follow it but are in the 174 to 216 MHz range. The real chunk of television channels (14 through 83) sit on UHF between 470 and 890Mhz. They are much further away from the FM radio frequencies and even further than the AM freqs than the first two chunks of channels which sit in the VHF bands.
So, as you can tell, you'll definately get improvement on TV channels 2 through 6, but 7 through 13 seem much more unlikely since the AM/FM antenna in the car is not tuned for 174-216Mhz, and almost 100% doubtful it will help for channel 14 through 83 since they're in the ultra high frequency band.
Really, you should consider getting a vehicular antenna that is rated for wideband use (meaning, it covers a wide range of transmission bands). There are several antennas that can cover as low as 50kHz all the way up to 1.2Ghz in one antenna. I'm certainly not an antenna wiz, I'm still learning. But having a dedicated antenna will extend your range incredibly as well, so you won't have to worry about the heavy interferance that is common with TV over the air.
I have even seen antennas that can be mounted inside your trunk sideways that will help, but they're not as functional since they aren't vertical, and they are closer to the ground.
Let me know if there's more I can help with if you choose to get a dedicated antenna. Antennas can certainly get expensive, but you should be able to find a really good one for somewhere between $50-100, and yes, cheaper ones exist, especially ones made by hobbyists. I just picked up a homemade antenna from Ham Radio Outlet that is two antennas inside a PVC pipe that I use indoors or outdoors whenever I need portability (not for car use, it's like 4-5 feet long) and it only cost me $20. Really improved my wideband receiver abilities. I recently heard a station transmitting from over 300 miles away! So as you can see, the antenna is one of the most important pieces of the puzzle, even though it only looks like a long piece of wire.