Thank you very much for your advice. On the first link you gave (Brother's website) it says that there are issues with Eero. The printer needs to connect to a 2.4 GHz network, not a 5:
Mesh Network
A mesh network is a type of network setup utilizing multiple wireless access points or nodes, within an environment, which appears as a single network. Though there are multiple wireless access points, they all broadcast a single network name (SSID), which allows for streamlined connection by multiple devices.
If you experience repeated offline or lost connection issues with your Brother machine, the mesh network’s name (SSID) must be separated into different bands and the Brother machine must be connected to the 2.4 GHz network.
Not all mesh network configurations allow for separating the network name (SSID). Please check with your device manufacturer for specifications and instructions.
EERO Mesh Network Users: We have found a link between EERO routers and Brother devices, which may cause frequent wireless disconnection. Our technical support team has thoroughly researched the situation and found that due to the specifications of EERO routers, we do not have the ability to stabilize their wireless connection with the Brother device. For a better overall network connection, we recommend using your Brother device with an Ethernet cable connected to your router, if supported by your machine's specifications. You may also use a USB cable connected directly to your computer. Brother cannot offer any further assistance with this issue while using an EERO router.
I will get more info from the Eero company.
Thanks again!