Id like to share all the exercises I did so far and also some Im about to do, to show you how complex such issues can be and that pencil pushups you found on the internet probably wont really do it justice:
-tranaglyphs with 3d (red, green) glasses - images that go futher and further apart (red and green image respectively) and I am trying to keep them fused, see peripheral points and checking for depth perception on each step, my vision being separated by the colored glasses. That is done by small steps timed by a metronome to keep a steady tempo and increasing difficulty. This trains endurance.
-tranaglyhps like in the previous description, but now only two steps a lot further apart, you jump back and forth. These train explosive power in the eye muscles and usually lead to better results in the endurance exercise before
-brock string (now completed), following a string from near to far point, keeping fusion, checking if I have input in both eyes, trying to fuse the point where the string crosses with the point where I accomodate
-accomodation on each eye separately, with the other one covered - switching two lenses in front of one eye for a minute at a time, refocusing through the lens on a text of specific size and specific distance. Future exercise is to do this binocularly, so to use both eyes at the same time.
-transparent card - the most recent and most fun, as it doesnt require any computer and makes me realize what Im trying to achieve. Card with images progressively further apart that you try to connect with depth perception first by converging your eyes in front of the card, and then behind (that for me is the problem, not enough divergence power and convergence overpowered). Then when the images fuse, you should also see them sharp (accomodate binocularly) and with depth perception (keeping proper eye vergence).
There is more exercises to come and Im about halfway done at best. As you can see, its a lot more complex than anything youll find on youtube or on the net, unfortunately. This is very neglected field but work is being done on it being more available.
Ive been using my new iphone 7 without glasses all day yesterday, got a bit of tension in the evening which went away quite quickly once I laid it down. I dont wanna get ahead of myself, but it seems to be improving day by day. Previously this would result in a migraine that I would still have while writing this.
I recommend you ask your specialist if they even know about these exercises, and if they dont, move on to someone else.