Personal conveyance does not affect the driver's on-duty time. It should go without saying, but personal conveyance is an off-duty drive status and therefore has no effect on the driver's available hours of service, or on-duty time.

Does personal conveyance count against reset?

The 10-hour break or 34-hour restart? Time spent appropriately driving under personal conveyance while off duty will count as part of a driver's 10- or 34-consecutive-hour break, with the requirement that the driver obtain “restorative” rest during the break.

Does PC Start your 14 hour clock?

Personal conveyance (PC) is an off-duty driving status, and counts the same as off duty for different availability limits. Specifically for the 14 hour workday limit when using federal US Rulesets, PC/OFF duty will count towards the limit counting down because it is a consecutive limit.