Pilot reported inadvertently taxiing into a restricted TSA area at STS Airport due to unclear ATC instructions and a lack of signage and airport surface markings to clearly designate the area.

Narrative

After landing at STS (Santa Rosa airport) clear runway at taxiway at A4; I contacted Ground Control on 121.9 for 'taxi to jet center' for parking. I could see it straight ahead off to the left which matched the airport diagram I was reviewing. Ground Control stated 'straight ahead'. I started straight ahead following the yellow taxi line; but after about 100 ft. I stopped because of construction equipment ahead and a faded red line. I called Ground Control and stated 'I think you made a mistake there is nothing but construction ahead' I did not get a response from Ground. I then heard Ground Control tell Person A in airport car #XX to tell the airplane in front of him to turn around. I called Ground saying I was turning around; but since I could not back up I had to cross over the red line which had not designated signage on the ground or post from the direction I can directly straight from A4. Ground Control then gave me progressive directions down another unmarked taxiway direct to another jet center on the other side of the Tower. The Ground Control car #XX approached me after shutting down and exiting the aircraft saying that I violated TSA incursion into a designated area. I mentioned that I was following instructions from the Ground Control and there was not the proper required signage and clear designation on the ground. When I saw that the instructions given by the Ground Control was not correct I stopped and asked for clarification. It was a safety violation by Tower Ground Control to direct me into a secure and hazardous area. It is also airport negligence for not properly designating the secure area. This is a safety and security concern that should be mitigated immediately.