Yes external car battery 9-14v can be used with a transistor driver. Best bet is use an automotive "low-side" or "high-side" switch. Single transistor stages can switch with a current gain of only 10 with rated switch low voltage drop Vce(sat).
Relays are about the same with a gain of 10 in the ratio of contact current rating/coil current rating.
When looking for power switches , remember this category...
Product Index > Integrated Circuits (ICs) > PMIC - Power Distribution Switches
Here is
one of hundreds of examples.. Read the specs fully and buy a bunch. They are cheap.. <1$ but far superior to any single stage transistor and did i say cheap?
Si3861BDV
Number of Outputs 1
Rds (On) 75 mOhm
Internal Switch(s) Yes
Current Limit 2.3A
Voltage - Input 4.5 V ~ 20 V
Operating Temperature -55°C ~ 150°C
Mounting Type Surface Mount
Package / Case 6-TSOP (0.065", 1.65mm Width)
This means you can drive them from low voltage logic levels to drive 2amps easily. LED reels start around 1.2 A