Hers is the solenoid relay I used:
https://octopart.com/586-903-white+rodgers-18775474. Unfortunately they are not manufactured any more, because, having a 15V coil, it was ideal for battery charging applications. They are available
here on eBay or
Amazon, but they are more expensive than the 12V replacement.
The Newmar part for your coach with Silverleaf is White Rodgers 586-902
here in Comnet. It has a 12V coil.
Amazon has some of the 12V ones
here.
Here's the technical reason why I think the 15V version is superior to the 12V version, at least in my application using a BIRD:
It has a 15V coil which worked well in my application with the coach being plugged in 90% of the time (12V coils don't like 14V being applied all the time). The 15V version will pick up at 11.25V and the
max rated voltage is 16.5V, ideal for a lead acid battery install IMHO. The 12V version is max rated at 13.2V, too low for the 13.8V float voltage required by my batteries.
Maybe the Silverleaf folks have thought about this and the TM102 does not drive the solenoid relay with full battery voltage all the time, but if you smell a burning odor from the relay you may want to consider using the 15V version, that burning odor is the result of the coil being overheated due to constantly being run over the rating.