How do I track if an invoice has been downloaded?

Firstly you need to ensure the Client Entry has been set to deliver the invoice as a downloadable link rather than as a PDF attachment, so you should check that is the case:

When invoices have been delivered from the site and the recipient clicks the link contained in their email to download the invoices the system tracks and records when that was done.  You can view this by checking the invoice from Invoice Display or Invoice Edit:

The green tick indicates the invoice has been downloaded and the cog icon next to it will state precisely when it was downloaded by the client.