My first thought would be a dodgy earth lead. First flick of the switch causes no action from starter due to high resistance. Second flick overcomes resistance due to heat build up at point of highest resistance improving the connection.
I would take all leads off, not just check they are tight, clean up the contact areas, smear with copper grease or vaseline and re-connect.
You know the vehicle will ultimately let you down at the most inopportune moment.
On my Ward La France the earth lead runs directly from the battery to one of the starter mounting bolts. Non of this earthing through the chassis or body first then a separate lead to somewhere on the engine. In my opinion the less convoluted the path and least connections for the electrons to get round the better.
Don't overlook the possibility that the leads themselves may have broken down internally due to age and corrosion. Test the resistance from one end to the other with a multimeter.