In series with output.
Trickle Charge R2 Value is (PSU volts - 14.2) / (Desired output trickle current).
But HOW does your charger work? Usually set to give a max current simply using a series resistance,
Main Charge R1 Value (PSU volts -10) / (Desired output current).
Where PSU volts is the AC voltage less 1.2V (silicon bridge).
No electrolytics are used.
Old models R1 is resistance of the Metal Rectifier! R2 only existed if there was a Trickle mode.
A Car Battery charger is MUCH simpler than NiMH (constant Current), which is MUCH simpler than Lithium.
There are such things as "Smart" chargers for UPS use and different kind of Smart Charger for Lead Acid disconnected from Equipment.
Only 6V & 12V car Radios (Valve, Hybrid or Transistor) or In Car systems can be operated while charging a Lead Acid Battery, stand alone Vintage 2, 4 or 6V vintage stuff not designed for vehicle use usually would be over stressed to be used while Battery is on Charge.