Hi David
I built Bill Smith's Gearless gravity arm clock which had a hip toggle sustaining mechanism. I tried to bypass his ideas by using readily available solenoids from the internet but in the end reverted to home made.
The design had two coils.
I used B&Q 'black' steel rod for the cores.
For the former end plates (1.25" diameter) I used discs of double sided printed circuit board Araldited to the core ends and with the copper hack removed to leave appropriate lands for the wire terminations. I used 0.55mm copper self fluxing wire for the windings and covered the core before I started with a layer of copier paper.
I built up layer upon layer in an even manner while rotating the former slowly in the lathe. Every second or third layer I put a single layer of copier paper. This gave a flat surface to start the next winding onto if I had messed up the previous layer. I finished off with a layer of self amalgamating tape which doesn't look pretty but made sure the wire was held firmly.
I had one clang while winding where the wire snagged and broke. I drilled a couple of holes in the end cheek as close to the winding depth so far and took the broken end out through the end cheek. I feed the broken end of the feed reel out and jointed it and then continued. This kept the joint outside of the winding mass so there was no exposed joint to cause shorts. That might sound a bit confusing and hopefully you won't have cause to do the same.
When complete the two coils had significant magnetic pull with little residual hysteresis. The current consumed at 12V was around 100mA and with the short period of activation (100ms) this was quite good to run from a battery for around 12 months.
Image below shows the development lash up. Ignore the curly wurly coils, they are just for effect. The cardboard shroud is to stop stray light affecting my Microset timing device light sensor.

Recommend Bill's book not just for this section and the concept of the design but also for his wealth of information on workshop techniques and tools. This is enhanced with his videos. Sadly Bill is no longer with us.
Kind regards
Alan