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With BJT transistors (ie, not FETs) you have to derive the series-Base resistance range from transistor specs (ie, its gain which is usually specified as a range eg 80-500) and from the load size.
FETS do not need input (Gate) current limiting whereas BJT (Bipolar Junction Transistors - commonly referred to as "transistors" even tho transistors include FETS & other types - needs to be of some minimum value (that limits current) but some minimum to ensure its resulting (Base) current times its gain (aka β = Beta) supplies enough current to the load. Then you add a Base to GND resistor and Base to input resistor that provide a Vb of about 0.7V blah blah blah....
Nah - transistors (BJTs) for simple amplifier designs, but (MOS)FETs for switching or digital applications like this. (The bonus is then the very high impedance (negligible current) of the FET's Gate etc.)
PS - because vehicles are typically 12V or higher, same sized resistors may work.
EG, if both our Gate-GND & input-Gate resistors were 1M and therefore a +12V "on" input (or 14.4V etc) means a Gate voltage of +6V (or +7.2V etc) which may be high enough to turn the MOSFET (fully) on. Certainly an L-type would - ie Logic-types needing input voltages under 5V for full turn on.
