Clip on heart rate monitors appear to be conventionally attached to the index finger.
Since the thumb has a feelable pulse (the reason you never check if someone is dead with your thumb on the carotid). Why is the thumb not a preferential digit for monitoring?
It’s probably too thick, or at the least, there’s no need. The “ET finger” pulse oximeter needs to see through the finger as its calculating the pulse and oxygen level optically with infrared light.
The pulse-ox monitors work by shining infrared light through the finger. The heart rate monitoring is more of an added bonus, but since it’s not always a very accurate measurement (varies based on fingernail polish, thickness of nail, placement, etc). If the heart rate, or more importantly the heart rhythm, is desired, you need electrodes on the chest.
As an aside, there are sticker ones that are more useful for longer term, or continuous monitoring.
It would work just fine on the thumb, but patients need their thumb to do stuff. Any other finger can be held away from what you’re doing (like picking up a cup) but you kinda need your thumb.
Pulse oximeters use two LEDs of different wavelengths to measure oxygen saturation/pulse. The signal is light that passes through the tissue. To make it work on thicker tissue, you need more powerful LEDs.
You can buy these things now for home use for about $12US. They’re handy when riding stationary bikes, and also nice to check out the efficacy of your breathing exercises.