To me, the way I understand question... the purpose of wanting a LED light is to see if burner is or is not on, while traveling on propane?
I went a slightly different route because I wanted to know what our actual frig/freezer temps were when traveling. And not in love with any open flame while traveling but that is talk for another debate.
What has worked out great for us is a wireless temp gauge. Didn't think the "wireless" thing would work going down the road but is works fine. Fridge at rear of trailer is about 42 feet from tow vehicle dash to fridge/freezer. In this link below be sure to read the comments and decide for yourself. Lots of reviews.
When we got ours I couldn't get it to work. You have to buy high priced batteries that will work in freezer and we can't hear the so called "warning peeps" over road and engine noise. But wife just takes a glance every so often. Beyond those problems, which we could care less about, the gauge has worked out great for several years. And we have found out that we don't even need to have fridge/freezer on when traveling on most days in our 2012 trailer. But in our older 2003 class C only good for about 4 hours. Also found out If outside temps are going to be above 75 then we just turn down temps colder before going to bed the night before. If you do get one of these... directions are not the greatest, just go step by step.
Batteries must be "lithium batteries (not included)" in the sensors, regular batteries won't work because of low temps. Especaily the freezer. Friends saw how good ours work and ordered one. Theirs didn't work right from the beginning. They returned it and no questions asked and replacement was within a week.
https://www.amazon.com/AcuRite-00986A2-Refrigerator-Wireless-Thermometer/dp/B004QJVU78The elec knowledge is great on this forum... I had help installing a LED so I could tell if I remembered to shut off water pump or not by just looking in my driver side mirror.
You might have other reasons for a LED light, but by the time and money and hassle your going to have invested putting in a LED...you might want to consider a wireless gauge.
Also at home when our elec goes out after a storm I put sensors in house fridge/freezer, so I know when and if I need to run extension cord from genny in RV to house stuff.
2003 Majestic 23P... Northwest travel machine
2013 Arctic Fox 25W... Wife "doll house" for longer snowbird trips
2001 "The Mighty Dodge"... tow vehicle for "doll house"