I have a '99 F-150 5.4L 2WD Super Cab, and I decided to put the Zenon headlight bulbs from my sister's '04 Ford Mustang into my F-150 after she decided to swap them for the OEM halogens (the Zenon bulbs were aftermarket). The bulbs are identical for both vehicles (9007) and the low beams work fine, but for some reason, when the high beams are switched on, one light goes out and the other one switches to high. The bulb that goes out was on the passenger side, so I tried swapping out the bulb on the drivers side, and it was the same problem. Lows work fine, but on highs, instead of the passenger side light going out, the drivers side went out. So, I know it's a bulb problem, and I wanted to see if they would still work in the Mustang. But, when I pulled the halogens out and put the Zenons back in, the low and high beams work fine. So what could be the problem?

 

I had a similar problem running high wattage bulbs in my truck, I think that it's because the connectors were pretty chitty, try wiggling the wires gently until they work, the pins were really loose in my connectors for some reason.
Wiggled them, and they worked for a while, but when I replaced the connector the worked fine.