ESR meters are great for measure the state of charge of Amp hr capacity of batteries too.
Mallory Energizer uses the method of measuring the voltage using two current limited sources 5 mA and 505 mA thus the difference in voltage is the ESR . It does this after 50ms of chemical equilibrium.
LiPo battery ESR meters use the max safe current of eight (8) watts ( dumped into battery ESR) per Ah capacity for testing batteries and from this you can compute the ESR and State of Charge.
I suggest you use the same approach for measuring ESR in shorted boards and capacitors. TO perform this you need a capacitor with LOW ESR ~ 1mOhm and a 100mV shunt resistor or 0.1V/0.5A= 200 mOhm and a switch gate pulse of 50ms with a Sample & Hold to measure the voltage after the discharge is opened.
apply 1mA measure Vf on 200mOhm shunt thru probes to target, when instrument reads 200uV it knows you made contact and then switches to 505 mA constant source
then charges up a S&H and turns off the power MOSFET in 50ms and takes the reading.
YOu can then repeat this every second to see if the ESR changes with probe pressure or probe position.
It is automatic if you sense 5mA then zap, hold, open ADC read and loop.
If you want to fuse the short open. Switch to a higher Capacitor voltage discharge and apply for 0.1 second so you do not waste much battery power. YOu can work out the I*t fuse time constant of the short you wish to blow and calculate the Joules of 1/2CV^2 required to blow the short, without burning up your tracks.
For inductive loads a back to back diode clamp will work without affecting the shunt reading.
extra [points] if you measure voltage rise during the current source to measure inductance, for limited range.