How much trust in your monitors do you need to feel comfortable with GTM failing over a Database backend?

Short answer is: a lot.

The long answer is that there are many things to consider, such as:

• the physical location of the GTM with respect to the database that it's monitoring
• the monitor you are using and its ability to accurately detect the health of the database server
• the reliability of the database synchronization solution in place (if applicable)

I'm sure I'm missing other key points, but these are three off the top of my head. Could you elaborate a bit more on your environment and your requirements?