The beep and clicking indicates you have a bad connection somewhere. Might even be a bad battery cable.... Check all major connections, power, and ground. Give 'em all a bit o' cleaning.

 

I'm not sure I fully understand you're testing. When measuring voltage drop you actually want a reading of zero. Voltage of any kind measured on the same side of the circuit indicates a connection issues. Think of your multi meter like a calculator. Your meter is actually two separate meters you only see the resulting difference of the two. The calculation is Ground Lead - Power Lead. !2v on + minus 0v on - = 12v. If you flip the leads, flip the equation, hence why you get negative voltage on your meter. Each lead measures voltage present at that spot. The + side should have 12v generally speaking, the - should be zero. When you touch one lead to each side you get 12 as that's the difference of the two locations. So in the case of measuring drop on a circuit you want 0. Any voltage reading other than 0 indicates drop or loss of voltage between the two points of measure. Battery cables, ends, connections, fuses, corrosion ect.

Measuring voltage across the battery doing nothing with the car is called static or rest voltage. When cranking your starter and measuring voltage you will get some normal drop. I say anything less than 10v while cranking is an issue, but not necessarily a bad battery. This test is best done along side an amp clamp but generally speaking people don't have or need a 500amp+ amp clamp laying around. I can do this test on my oscilloscope and layer voltage with amp draw and actually see each wave of amp pull/voltage drop with each winding rotation. Help locate other possible issues if its not the battery. This test could even be layered with the cam position or crank position sensor and you can see each compression stroke's amp draw as a digital compression test and locate the bad cylinder.

I drew a crude diagram of what you're measuring, I am not an electrical engineer or an artist so keep the critics on your counter
A reading other then what I have written indicates a problem to be addressed. It may not be of immediate concern though.

 

I agree with everyone else. Without a load test you're just guessing. Had my motorcycle battery on a trickle charger. Tried to crank and just clicked. Put it on a charger overnight. Measured 13v static. Left the voltmeter connected. Tried to start it, voltage dropped to 7v. Bad battery.

 

First, even though the battery was at 13 volts, got out the jumper cables and hooked it up to a running car to make sure there was enough power and the results were exactly the same. Second, even a battery that won't supply the required cranking amps will power the radio. It also won't cause the dome light to go out, stay out, and then start working again if you disconnect the battery for a while and then hook it back up. I appreciate the suggestion but this is a problem with a relay or module or something.

 

Thanks, but as stated in earlier posts I've already done all that. The cables are good, no voltage drops anywhere.

 

Your symptoms tell me you do indeed have a bad connection somewhere. Those are classic symptoms. Start testing to WHERE the power drops out when the problem presents itself. Start at the battery, and work your way down stream.