Double check that you used the correct bulbs. If you used heavy-duty brake bulbs in place of plain old bulbs then that may cause the problem. Or if you used a combination "brake and turn signal" bulb then that may cause the problem due to having two contacts on the bulb instead of one.

The bulbs are the same shape, so it's easy to get the wrong ones.

I presume the problem didn't exist before the swap and now it does? You could also try to isolate the problem by selectively unplugging one corner at a time.