[Tom Goldman]

Current draw would only be an issue if the starter was actually engaging and trying to turn the engine over .
The starter relay only clicking can be the result of several issues , the most common one I see is voltage drop across battery or starter cable connections , especially ground cables .
Start with fully charging your battery and having it load tested to confirm it is up to par .
Check for voltage drop at various points of both positive and negative sides , starting at the battery posts any working toward the starter .
You should test both at rest and while cranking .
Cable ends that have not been properly crimped and soldered are the worst culprits . Clamped or compression type lugs should be replaced with crimp and solder connections .