Hello again Martin,
Yes an (your) alarm / immobiliser will flatten the vehicle / engine battery over a few weeks if not ‘float’ charged.
I am surprised that your solar system is not compensating for this expected drain whilst your assumed faulty battery charger is not.
There are ‘add on’ modules available such as Battery Master or Battery Mate which will transfer any excess solar charge to an engine battery once a leisure battery(s) is considered saturated (charged). Trust me, no such ‘add on’ module is necessary in any type / year Hobby if the installed solar system is wired and connected correctly.
To save any unnecessary time and expense, do remove both batteries (expect to drop the contents of the boiler on doing so) and attempt to recondition them individually.
I repeat, it is impossible to read (achieve) any more than 12.7 volts terminal voltage, 24 hours after a period of rest from a charged a lead acid battery.
As explained in my previous reply, the vehicle engine battery only receives a trickle charge once the leisure battery(s) are satisfied (saturated), when the green light is on at the control panel. This is a one time (one shot) process. If the power supply, normally via the hook up is interrupted, only for a second, the process starts again from scratch. Albeit, after a few seconds interruption, it would be shown as a short period of initial red, followed by another longer period of amber, then back to green on the control panel LED once the charger realises where it is at in the process. Only then does the engine battery receive a trickle charge.
In your case, ignoring any problem with the Toptron charger, your solar panel should be keeping your engine battery charged.
Your type of Toptron charger needs to see a healthy leisure battery(s) before it can get to the end of that process.