As GRJ says, you'll probably need to "tune" the value of the resistor. 1K is simply a starting point to get you in the ballpark. Note that adding the red marker LEDs plus resistor off the end of the LED strip will siphon current from the white strip LEDs. So if you already had a desired brightness on the interior lights, you'll need adjust upwards the control on GRJ's board.
Most guys probably don't have a stash of resistors lying around to "tune" the marker brightness. That is, you might just have purchased a pack of 10 or 100 1K resistors. Note that for experimenting, you can simply put 2 1K resistors in series to get 2K (which will about half the marker brightness), or put 2 1K resistors in parallel to get 500 (which will about double the marker brightness).
Or, if you see more DIY in your future, why not get a resistor assortment for less than a penny per resistor (free shipping from Asia) which includes 1K and other values - one of which will surely be suitable for the matter at hand.
But back to the red LEDs.
Another reason you'll need to tune the resistor is there is a substantial difference in brightness (for a given current) between red LEDs. I've found the ceramic stem type (bottom of photo) that GRJ mentioned earlier is a good performer but kind of spendy (over $1 each?). As the photo shows, there are options though hard to suggest a specific component without seeing the mounting or space constraints of the particular passenger car.
I'd think some cars might even accommodate the widely-available 3mm style for less than a penny per LED 
