There are 2 reasons why you would not want to use the factory EGT probe with a gauge.
#1 - it's too far away from the exhaust ports to make any difference. It's actually AFTER the first catalyst. The reading here will be several hundred degrees lower than what you really want to measure.
#2 - it's not a precision sensor. It's not there to tell the ECU the exact EGT values. It's just there to monitor the temperature/function of the catalyst to make sure it doesn't overheat and break. It's there to protect the cat, not read accurate EGTs.