Check the L3 Illuminations with Nichia
I have one (L11C). I really like it because mine has the Nichia high CRI LED, and is simple and very compact.
However, I would not consider it a great car light because the button is small enough to be hard to press with gloves on, and it has a bad reputation for withstanding drops.
A headlamp is also my personal preference. I'm not sure if I've seen a small clicky, $20 flashlight that strikes me as particularly well suited to automotive work. I was tempted to say the Thrunite T10, but I don't think the wide mode spacing would be great for the purpose. Maybe an Inova X1? It's a simple 2 mode light.
The Fenix E12 is in a very similar class. From what I recall, it has a very tight center hotspot that might be good for seeing into nooks and crannies, but not as good at illuminating the whole engine compartment.