What's wrong with my static relay connections?
The relay is a photo triac circuit and the "contact closure" may not be easily proven with a multimeter because there will likely be not enough voltage generated by the multimeter test leads to overcome the forward volt drop of the triac when it conducts.

Here's the general idea: -

http://www1017.vu.lt/legacy/pfk/funkc_dariniai/images/triac_iv.gif

Without significant current to pass the minimum holding current (a few mA) the meter is unlikely to register anything other than a bit of leakage current. Also if you read the data sheet, the load current range is 0.1 A to 2C and no way will your meter meet the minimum requirement.

Having said all this, please double check you have the photodiode polarity correct - if you think this has been wired incorrectly at any time there is a possibility the device is damaged beyond repair.