At times the starter will not engage

Until the gas gauge and temp gauge move. The gas gauge for sure. The ignition has power as the accessories work. The happens virtually every time in the winter. If the interior is warm it may be only a slight delay, couple seconds. If left for a few hours or more then it may take several minutes before the gauge moves and then it has power to the starter. It seems as if there may be a solenoid of some type that supplies power to the starter circuit that is getting stiff or worn out. Any suggestions?
Thanks