I don't have enough of an understanding of HVAC to know if the pictured boiler fuse box is considered a control panel or a sub-panel – but some wiring issues there lead me to needing to understand more about this setup – and how to handle the unattached ground wires.
Notice at the mid-left and mid-right there are two grounding wires that are not bonded to anything. One is the NM cable with bare copper that runs to the boiler on-off metal switch box – where it is bonded at that end in the cable clamp. The other is the green wire coming out of the block-like device [transformer].
That same unidentified device [transformer] seems to have it's hot and neutral wires reversed at the ceramic fuse block: the white wire tests "hot" with tick tester, same as another black wire terminated there.
Both the cables that feed this fuse box (20 A), and the devices below it (pump relays?)(15 A), are old "BX" and do not appear to contain any bonding strip. The junction boxes they originate from are bonded to grounding wires that run back to the main panel box.
That ceramic block that holds two 15 A fuses appears to isolate the neutrals from any ground connections in the box – if they'd been connected. As it is, it appears the only grounding means is via the armor of the BX cables.
So how should I handle the unattached ground wires?
If anyone is open to discussing the control panel at the bottom of the box I'd love to add some more pictures and also ask about that. Even a link to a resource that educates about a setup like this would be appreciated.
Best Answer
Add a ground screw and land the ground wires there
I'd use a self-tapping ground screw (Garvin GSST or equivalent -- these are different from regular sheet-metal screws in that they use a fine-pitch (32tpi) thread instead of the 16tpi coarse pitch thread normally found on a sheet metal screw) into the back of the box to provide a grounding point, then land the loose ground wires there. The fact that it's only grounded via the BX armor is not great, but it's better than floating altogether....