Hi there, @Nutch3.
Let check why your accounts form your QuickBooks 2016 aren't showing up on your QuickBooks Desktop (QBDT) for Mac 2019.
One possible reason why your accounts aren't showing up on your QuickBooks 2019 is because of the company you've opened. Please ensure to open the same company file, or create a back up of you 2016 file and restore it to your QuickBooks 2019.
To create a back up of your company file:
Once completed, restore the file to your QuickBooks 2019.
For further details, you may check this article: QuickBooks Mac Create a Backup of your company file.
You can also download our QBDT Mac 2019 user's guide for your future reference: QuickBooks Desktop for Mac 2019 User’s Guide.
I'll be right here to help you if you have any other QuickBooks questions, just add a comment below. Have a wonderful day ahead!
Open and convert your company file.