I've pieced together this circuit but I'm not sure if I've got all the connections right...

Here's what I'd like it to do:

When triggered with S1, U1 delays approx 10 secs before triggering U2. U2 then outputs a signal activating M1 for approx 3 secs before shutting of again.

Does it look workable?

 

looks pretty good to me.

one question though... why two 555s? why not a 556?

 

Yeah, I might do that later - I wanted to make sure I was on the right track first.

Does the switching transistor in U2 and S1 look right? Those are mostly the things I wasn't sure of. Also pin 7 on U1 - it looks like it's not connected to anything?

 

Nope, your circuit has some problems.

Try it like this:

C5 is optional. It was mainly to enable the circuit to operate under simulation without having to add SPICE controls.
If you leave C5 in, it will cause U1 to trigger when you first power it up.

 

Thanks,

I definitely don't want U1 to trigger until S1 is pressed so I'll leave it out.

I assume c2 is 1 uF?

 

Thanks,

I definitely don't want U1 to trigger until S1 is pressed so I'll leave it out.

That's fine.

I assume c2 is 1 uF?

No, it is 1 Nanofarad.
1uF = 1000nF
Conversely,
1nF = 0.001uF

There is also Picofarads.
1uF = 1,000nF = 1,000,000pF
0.001uF = 1nF = 1,000pF
0.000001uF = 0.001nF = 1pF