What made the connection between special relativity and general relativity is a simple observation. Einstein didn’t tell me but I realize.
special relativity: if you are moving fast all processes will run faster because now you have more energy. [just like you run more when you have more energy and this is applicable to time, special case time dilation, time runs faster because more energy is available, eg when a clock is in spaceship, intuition: this insight could have come to Archimedes. Nothing special, it just didn't, sometimes it takes 2000 yrs to realize what we have really understood, Einstein did this but Newton could have done time dilation in terms of classical mechanics]
The connecting link: now that time and any process runs faster because of more energy they would run slower if less energy is available. SO a force that stops gradually, the motion, will reduce the rate at which any process/time runs. This would be time contraction. [just so that energy is conserved time-units and length units etc are readjusted. eg in a complicated situation everything would readjust and every situation will have a different time dilation/contraction formula ] The connecting link is since deceleration has reduced the time rate [time contraction] all deceleration are equivalent to something that causes clocks/time to run slower. We would know that time runs slower in Gravitational fields because less energy is now available [reverse if you are escaping a gravity field, see how easy redshift etc are]
So deceleration is equivalent to a gravity field. Which is exactly what principle of equivalence of Einstein is. ‘In some paperwork” I have proved this equivalence from classical mechanics. [only from Newtonian formula for gravity].
This means many special and general relativity ideas are actually also classical mechanics ideas but Einstein extended them and made them more general, exact and advanced. eg Einstein studied them in more situations than were studied before. Time dilation, equivalence principle and gravitational dilation are all simple classical mechanics ideas. All the details I have written in recent articles in in this website check last 1-3 months under Relativity/Physics tag.