What are the best ways to test the integrity of your E39 head gasket?

Lately, it seems that more and more E39s are succumbing to head gasket failures, especially from those owners wholly unaware of the cooling system time bomb; and it seems more newbie owners are buying used 'affordable' E39s ... which end up having head gasket problems from the start.

Therefore, it behooves us to have a thread to point people to where they can easily test the head gasket, either before purchasing a used E39, or after.

Based on research outlined in this thread:
- My E39 overheated & I need a new head gasket (1)

It seems there are at least these methods of testing an E39 head gasket:

• Cooling system "geyser test" (1)
• Cylinder compression tests, wet & dry (1)
• Cylinder leak down test (1)
• Cooling system pressure test (1)
• Cooling system exhaust gas analyzer test (1)

For the record, so we can point others here, what tests (details would be nice) are good to run on an E39 to check for head gasket & other overheating-related problems?

This leak tester seems to be priced in the DIY range (if it works):
- Who here has tested the E39 head gasket using an exhaust gas analyzer on the coolant?, by bluebee