Where/source for the synaptics mousepad driver?
Are you manually downloading, installing, and configuring the driver yourself?
No third party installers or apps - correct?
Look in Task Manager > Start up and also look in Task Scheduler for any other unknown or unidentified apps etc. that may be involved.
Lastly, take a look in Resource Monitor/History. Very end user friendly and the time line format may reveal some pattern.
Something that is being captured/logged every second time you boot the laptop.