I had to do a similar test with about 1000 lines on a complex flex circuit. I used some FPGAs (Field Programmable Logic Arrays) that implemented a 1000 stage shift register. The shift register implemented a rotating bit (1 on, 999 off) that started at one end and stepped bit by bit to the other end. Each shift register stage drove an FPGA I/O pin that could be set to provide a weak pull up to Vdd. Each pin could read or sense the actual output signal and logically compare it to the orginal rotating bit pattern. If there was an difference, the controller would stop and then determine if there was a short circuit to circuit common or to another output by examining the states of the I/O pins. This scheme didn't determine actual resistance as the faults essentially short circuits.
I didn't have access to the both ends of the flex but in your case you could implement a checker that drives one end of the cable and reads the other. In the simplest case the receiver could be 24 LEDs and the driver a hardwired shift register, a rotary switch or even some test points that could be scanned manually. Note that this scheme requires that the driver provide a connection to either a test voltage or circuit common.
Hope this makes sense,
Cheers,