The current version of Streets & Trips has no feature that would allow the user to customize, or use own, GPS location icon.
Many years ago, I attempted to find a way to do it. It involved using a freeware named Resource Hacker http://www.angusj.com/resourcehacker/
to locate, and then replace, the .BMP image resource within one of the Streets & Trips files. If I recall correctly, the S&T file which contains the .BMP resources is the MSM(version number)USA.dll file. But I may be wrong, since it has been a while since I played with this, and it was a much older S&T version, too.
Having said that, I'm pretty sure if we read the Microsoft EULA, we will find out that modifying the program files is not allowed.