I'm sorry, but I couldn't reproduce that. I've created a new vanilla game, saved, then enabled miniMAXIme and loaded that save. The button was visible and opened the GUI. However, there's one recent change that could cause that: If your saved game is based on a scenario where you're not supposed to have a character (e.g. the vanilla "Sandbox" scenario), the GUI toggle button will be removed.
Are you using my helper mod? (You should check your mod list, some of the character mods require it.) If not, please install that mod and make sure you have at least one additional character mod as well. On loading a game, the helper mod will print some diagnostic messages if it doesn't find an active selector mod.
If installing the helper mod doesn't get you any further, could you upload the saved game (without miniMAXIme) somewhere and tell me what other mod mods you've added when you tried to add miniMAXIme?