Hi Dcneuro
welcome to the Apple (user-to-user) Community!
Re: "Voice control in accessibility does not work"
Sorry for the difficulties you have been facing in your use of Voice control. If the experts in Apple's accessibility team have not been able to help, I'm not sure whether there's anything much we can do to help.
Am no expert on Voice Control, yet your post to the community deserves some response.
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Re: "There's now been five updates, none of them have addressed this problem"
Seems you are using MacOS Sequoia on your iMac
Wondering if you have the latest version ?: What's new in the updates for macOS Sequoia - Apple Support
Eg: macOS Sequoia 15.5 : This update includes enhancements, bug fixes, and security updates for your Mac.
Wondering too, whether you have checked through Apple Support's latest articles for Voice Control using Sequoia: The way accessibility features work sometimes changes as they are updated, as with all technology., yet you likely know more about that than I do, as far as Accessibility features go.
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Re: "Since Sequoia, commands do not work.".
Seems not everybody who uses it has difficulties ? I could be wrong. Is this how you are using commands ?
For MacOS Sequoia: See how to: Use Voice Control commands to interact with your Mac - Apple Support
Eg: says:
"When you say commands in quick succession — such as “Scroll up”, “Move cursor right 5 pixels”, “Press OK” — pause about half a second between commands.
Tip: You can use the interactive Voice Control Tutorial to get familiar with Voice Control and practise essential commands. Choose Apple menu 
> System Settings, click Accessibility 
in the sidebar, click Voice Control (you may need to scroll down), then click Open Tutorial."
There is much more info. in the complete article that you can open from the link above.
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Re: Correction does not work"
There's a MacMost Third Party (non-apple) Video that may help: : 20 Voice Control Dictation Tips
https://www.youtube.com/watch?v=PWx64HznFiU
In supported languages, you can: Use a custom vocabulary with Voice Control on Mac - Apple Support
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Re:" Frequently the mic is listening but the Mac becomes entirely unresponsive unless you turn voice control off and back on."
See: Customize Voice Control on Mac - Apple Support
Eg: says:
" ... you can customise settings such as the language you use with Voice Control, the microphone you want to have listen for commands, options for showing item names, numbers or a numbered grid on the screen, and more.
You can also turn standard commands on or off and create your own commands, delete them,
and import or export custom commands."
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Resource: Complete User Guide: (There's a Table of Contents, and you can use the "search" field provided):
Voice Control, Switch Control, and Accessibility Keyboard User Guide for Mac - Apple Support
All the best :-)
