Older Zenith motion activated flood light not working properly
Replace the Fixture
In this particular case, since the red light flashes, it sounds like the sensor is OK but it isn't activating the relay for the light. But on an older halogen unit it is not worth repairing - just replace it with a new LED fixture. The electronics do wear out over time, especially with outdoor fixtures, and you will save money on electricity with a new LED fixture.
Look at the existing bulbs to find the power (watts) used and then translate that into an equivalent LED. For example, if your existing fixture has 2 x 100W Halogen bulbs, that is roughly 2,000 to 2,500 lumens according to this chart. Replace it with a new fixture like this one picked at random from Home Depot and you get 2,400 lumens for 26W. At 0.13/kWh (average US according to a quick search), saving you $8.25/year for each hour/day that the light is on (motion detected -&gt; lights actually on; the motion detector (old or new) uses very little power).