The LEDs are switched by open-collector transistors or Mosfets, and not relays. The semiconductors dong the switching are imperfect and have a leakage current. The leakage current is not enough to illuminate a tungsten bulb, but is enough to illuminate a LED due to the difference in impedance between tungsten bulbs and LEDs.
Yes, fitting a 120 ohm resistor to bring the impedance down to, essentially, 120 ohm and thus consume 0.1 amp is a possible solution, but is totally not necessary in this case. And it will dissipate 1.2 watts of heat, which can be a real problem in a confined space like an interior lamp holder as this can become hot enough to melt plastic.
All you need to do is bring the impedance of the LED down to a value where the “off” voltage across the LED is below the illumination threshold, and thus something between 1kOhm and 20k to 50 kOhm, 1/4 watt, is all that is needed.
Such resistors are small, lightweight, dissipate extremely little heat and cost around 10 cents if that. Often, 10c gets you a pack of 10 resistors.
A 120 ohm resistor that consumes 0.1 amp at nominal 12V dissipates 1.2 watts, and will get hot. You will burn out a 1/4 watt 120 ohm resistor and this you need a larger, wire-wound and often metal-cased 5W resistor, and these are sold in automotive shops for stupidly expensive prices, such as a few dollars of even 10s of dollars. My local DIY hardware store has them at something like $20 each! Crazy, when a 10 cent component does the same job.
A 1200 ohm (1.2k) resistor consumes 10x less current and dissipates 10x less heat. So only 0.01 Amps and 0.12 watts at nominal 12V. While it is only 0.12 watts, a 0.25 (1/4) watt resistor is fine. Take the resistance up to 12k, and the consumption drops to 0.001 amps, and power is 0.012 watts. Thus even cooler, and using less power.
So you see that any resistor higher than about 1k ohm doesn’t need to be bigger than 1/4 watt, and thus doesn’t need to cost more than 10 cents.
And the 1/4 resistors have long enough leads that you can often just fit them into the same bulb holder as the LED lamps, in parallel with the LED lamp. Thus easy to fit (albeit sure a bit fiddly, but needle-nosed pliers will help).
The only place you need a 120 ohm resistor is when you MUST show a 1.2 watt load to the controlling circuit. These cases are where you have bulb monitoring circuits that expect a certain load. This is what is often labelled as “CAN-bus LEDs” or “CAN-bus safe LEDs” or some other stupid marketing name. They are not CAN-bus LEDs. They are simply lamp circuits that are monitored for the expected load. And as you don’t have interior lamp bulb monitoring showing driver error messages, you don’t need to ensure you have a 1.2 watt load.
Sure, you can dig a hole to plant your tomatoes with a bulldozer. But why bother when a simple hand trowel is enough for the job?
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