No, that makes no difference. The 'Tait' programmer is unofficial and not guaranteed to provide the correct timing or voltages to the PIC so results will vary. Most of the Tait designs are for 16C series, not 16F devices although they are similar.
Most likely the problem is that you have set the configuration fuses for high voltage programming (on MCLR) but the Tait programmer is not able to provide enough voltage to put the PIC back into programming mode. Check the VPP voltage, it should be stable at around 12.75V when you try to program the device.
Your best solution is to buy a Pickit 2 or Pickit 3, preferably the genuine one or at least a clone with proper programming voltage generator on board. They are not expensive and can do a lot more than Tait's design is capable of. Beware of clones that only produce fixed VPP as it seriously limits the number of devices they can program.
Brian.