Shelly Dimmer2 - Control with Shelly Button1

I've been testing the same setup, but using Home Assistant as the middleman.

To save battery, tThe Shelly Button 1 has to wake up the wifi radio and connect to your access point each time the button is pressed. In my case, this means a delay of 3-6 seconds, and sometimes as you said it just doesn't work at all.

For the purposes of a light switch, this is way too long and the button is practically useless to me.

Luckily I only bought one for testing.

I'm installing extra switches around my house as "soft buttons" for for the purposes of either virtual 2-way switching a light, or controlling multiple lights together in a scene. I'm using the SW2 input on a Shelly Dimmer 2 for these. This does nothing to the light on SW1 as the dimmer is setup in Single Switch mode, however it does send the button push event to my Home Assistant server, which can then do what I've programmed it to do (turn on a lamp on a smart plug, turn on all lights in room or something similar). You can do something similar directly with the Shelly Dimmer using "events". This may not be of use to you, but I think some kind of hard wired button is really the only option for reliable, responsive light switches.