Bulb Brightness vs. Resistor Values

I have some switches in my car that use 1.2W T2 12V bulbs. When the parking lights are turned on, they all illuminate, but very dimly. There is a resistor in the circuit path prior to reaching the bulb so they don't glow at full power. Turn on the switch and then power is shunted to a contact between the bulb and the resistor so that the bulb illuminates fully. I wanted to brighten them up a bit, so I popped in some 2.1W bulbs, and they barely work - switch on or off. I thought they'd at least work in the switch on position, but they barely illuminate, not nearly as bright as the 1.2w bulbs while the switch is off! That does not seem right, but I don't know much about how resistors work in this configuration, but they've gotta be negatively impacting the the 2.1w bulb function. If I did want to use the 2.1w bulbs to brighten the switches up a bit, I assume I need to change the resistor. I can dismantle the switch and the resistors are actually easy to get to, unsolder, and resolver a new one. I was too dumb to note the value of the resistor used for the 1.2w bulb though when I had one apart. How does one calculate the potential brightness of a bulb based on the resistor to be dim when the switch is off, but let's just say maximum brightness when the switch is on? Thanks everyone. And FWIW, I do have a multimeter and a 12VDC power supply, so bench testing is readily available.