Any suggestions on how to mount this clock using only a single mounting point?

It has a pendulum so it needs to be relatively level. I tried to run a piece of wire between the holes hoping to fish a piece of string or something to create a triangle for mounting but no such luck.

A wire between them is what would make sense. What caused the "no such luck," and why can't you use two screws?

Could you screw a piece of wood into the one hole and then put two hooks into the wood?

No such luck was i was not able to get the wire from one home too the other.

And as far as two screws is i am using mounting hooks as they only make a very small hole in drywall rather than two big holes for screws and drywall mounts.

Carefully drill a centred hole between the two existing ones on the clock to hang it from?

Hmm. Is the mounting plate with the screw holes removable? If you could flip it so the notch is facing down and drill a hole in the middle that might work.

How heavy is this clock?

Laser level is by far your best option. Get a cheap one online.

Okay so you use (2) of those things. Do you have a level? If so put the level on the back of the clock over the mounting holes but where you can still see them. With a pencil mark the level where the mounting are. Now you have a template/ measurements for the mounting holes on a level. Now take that level and hold it on the wall where you want to mount it. Hold it level. Find your two marks and mark the wall in those locations. Now insert your little pokey hooks in the wall and hang.

It is not removable, it is all part of the "clock" assembly.

It is not heavy at all.

If its got a pendulum, you probably need the two anchor points to keep it from swinging.
If not, you could run a wire between the two points here and hang on a hook. Could drill a new hole in the middle of the mounting bracket and use that. Three hooks and a wire - one in the wall two in the holes and wire between, A spring between the two points could help with tensioning then add a hook in the middle.
Epoxy it to the wall.

I did not even think of it needing the two mounting points because of the pendulum.

If this is like similar clocks I've seen, the pendulum is only esthetic and has almost no weight. The friction of the clock resting against the wall would be more than enough to counteract any forces the pendulum would exert. Two holes shouldn't be necessary, but it will have to be pretty close to level for the tiny electromagnet to work.

Remove the face plate to see if the void underneath the mounting bracket might allow you to drill a hole to create a mount.

That's unfortunate, maybe as someone else said you can make some sort of "adaptor" using wood? All the best mate

Well, with wire, you can thread it through the holes and then wrap it around itself.

But here's an alternative. Get a couple of pictures hooks, something like this . Tie one onto each end of a piece of string or wire. Put the hooks into the holes on your clock, then hang out over the thing on the wall.

wire tied to each hole. Mount from wire.

though, if you can't do that.

1. painters tape on wall
2. use a level to draw a line with a black marker on the tape
3. tape on clock bracket, mark the centers of the holes by punching a small hole
4. pull off tape on clock and apply to tape on wall
5. line small holes with line from step 2
6. drill and mount

any kind of twine (nylon, fishing, or a shoelace or even just the wire insulation without the wire) that will fit on both holes, make sure to give some slack before tying on both holes (maybe around 1.5 inches), after that precisely find the middle of twine and tie a loop.

edit: if i wanna go more crazy for this, it seems it has screws, i'd unscrew those, take a ruler, get middle point and drill or solder a new hole.