I have a La Cimbali Junior S/1 Espresso machine (2002).

As nice as it is to have the flexibility of a tank, I would like to have the option to plumb the machine in.

As I see it there are three areas to address:
1. Drip tray
2. Empty tank safety circuit
3. Mains water supply

Drip tray
A drip tray that has an outlet to a drain is a standard component for the D series that can easily be purchased and retrofitted.

Empty tank safety circuit
The S/1 has a safety system to prevent against an empty water tank. It consists of a pair of wires that are suspended in the water tank allowing a very small current to flow. When the water level goes too low the current stops and so does the machine.
My plan is to measure the resistance across theses wires and then to install a switch inside the machine that allows me to switch between the wires and an appropriately large resistor.

Mains water supply
This is where I need advice. Installing a valve that allows me to switch between the tank and a pipe to mains is easy enough, but I am concerned that the pressure of mains would simply be too high. Given that the machine is designed to suck water from the reservoir using the vibration pump I'm concerned that any pressure on the water at all would be too high.
If this is the case then I'll probably opt for an auto filling approach. Something akin to mechanism that a toilet cistern uses to prevent over filling, though most likely I would go for an electro-optical rather than mechanical solution.

Does anyone have any information or experience in this area that might help?

Try Converting a pourover espresso machine to direct connect

Excellent! Thank you very much.

For the drain, be certain the drain tube maintains a negative slope after exiting the bottom of the machine--avoid the tendency for the tubing to create a valley or and 's' shape which will not allow the machine to drain quickly and completely. In my particular set-up, I found it was helpful to wedge a small wood block between the machine bottom and the tube to keep things flowing down. Depends on how high you adjust the feet, which are near their highest level in my case.

Bill