Try this test bushy,

This is part of my test procedure for a suspect solenoid.
Prove the coil has continuity and measures a resistance value (value should be in the manual you posted).

If the coil checks out, connect a known good battery 12 Vdc to the coil, whilst measuring the continuity across the main contacts, like my image.

[Linked Image]


From what you have said your battery is fine, maybe the coil is energising and becoming an electromagnet, like it should, but the contacts are seized inside & not closing, which does happen.
If all is good, you should measure a very low resistance across the main contacts, like 0.1 Ohms.


Happy is he who penetrates the mystery of things.