Frame advance will keep the emulator paused but advance one frame when pressed.
This is different from pausing the game using the Start button. The pause key will pause the emulator, freezing it in time. Go to Settings > Hotkeys and set Pause / Resume and Frame Advance to whatever hotkey you prefer. After all, in real-time, using the TAS Input Panel is harder than just using a controller. Using the TAS Input Panel has already been discussed above, but there’s more to TASing. In the Buttons field, you can click a checkbox to toggle whether or not the button is pressed, or right-click to toggle autofire. You can also drag the joystick by holding click, or right-click to toggle automatically follow your mouse cursor. You can click the analogue stick section to move the analogue stick, or change the numbers for X and Y if you want to position the joystick precisely. This is called the TAS Input Panel, and is how you do controller inputs when TASing.
You should see a second window open up that looks like this. Now, click the drop-down menu for RSP plugin and select RSP emulation plugin. If you plan to do real-time gameplay on Mupen64 and not just TAS, click Config below the drop-down window and set your controls. Start by clicking the drop-down menu for input plugin and select TAS Input Plugin 0.6. To start with, before you even load the SM64 ROM and start playing, go to Options > Settings… or press Ctrl-S.