Timer1 not working with external crystal (PIC16F628A)
Ok, I've build the schematic with a PIC16F628 non A, and after several crystals I found a few that worked. Out of 9 I own, only 6 worked. Resistor values tried ranging from 10K to 1M ohm, capacitors from 10p to 47p, didn't make a difference. It either just works or it doesn't. Some crystals are new, some were salvaged. Some new ones didn't work either.

I use xc8 v1.40. I used an external osc of 10MHz. The pickit 3 programmer has a hard time programming the PIC16F628 when an oscillator is connected. I have no problems with more advanced PIC16F1827 and PIC16F1937. 

This is the Timer1 configuration I used succesfully:

T1CONbits.T1CKPS = 0;        // Set Timer 1 prescaler

T1CONbits.TMR1CS  = 1;
//T1CON.TMR1CS  = 0;      //RJ Use internal OSC for testing
T1CONbits.T1OSCEN = 1;
T1CONbits.nT1SYNC = 1;
T1CONbits.TMR1ON = 1;


I didn't check if the timer gets incremented, but I assume if the clock signal is visible on the oscilloscope as measured on pin 15, it should work. Let me know if you'd like me to test this. I'll have to hook up a serial port to read out the values though.

I also read in Microchip errata documentation that PIC oscillator circuits can be a bit picky on the crystals. This seems to be my experience as well. I even saw a PIC32 "defeatered" as to supporting secondary 32KHz crystals. It may be more reliable to build your own oscillator circuit and feed in into the Timer1 T1OSI pin.

My advise: buy some more crystals and from different sources, brands and batches.