Crystal circuit works in breadboard but not in perfboard
Your plug type proto board adds capacitance to each node of the circuit that is greatly reduced when you attempt to duplicate the circuit onto the perf board. It is likely that the 15pF capacitors that you show on either side of the crystal may not be the correct capacitance in the perf board version of the circuit. You could try increasing the values to 18pF and then 22pF to see if either change would get your oscillator to settle down and operate at 32.768kHz as you expect it to. It may even be necessary to try 27pF or 30pF as well and it may even be necessary to use different values at each side of the crystal.