Homebrew PCBs

That looks like an impressive setup - especially for home use. As
someone who has worked around this type of equipment for 15 years - my
thoughts are you should put the entire machine in a secondary
tray/container. Because eventually - all etchers will eventually leak.
It may take a few years, but eventually it will happen to all
ethchers. I'd use a large try that's a couple of inches deep. Ideally,
it should be large enough to hold the entire volume of etchant in your
machine.

In response to your question about silicone sealant - some types
require 24-48 hours to set. But there may be a chance it is too old.
Most of the GE brand silicone RTV sealants I've used have a 2 or 3
year shelf life.