The 0-10v output IS the AVI/ACM.
It's just the term used when describing the analog voltage OUTPUT. I suggest you do some research before doing damage.
Your 24v to the BOARD has basically replaced the 10v POWER OUT pin on the vfd.
You can test the analog AVI (0-10v) and ACM (GND) using a cheap voltmeter or a 12v bulb + =AVI, - =ACM.
The reason I suggest a relay is because of the vfd shared common. It will be sharing 0-10v and 24v GND's which isn't normally recommended.
Newer vfd have separate commons and 24v internal control circuits. These you can directly connect with no problem. Those are what you are likely seeing any diagrams for.