How do I connect my other 2 DVR receivers using an Ethernet cable?

You have ONE Uverse DVR.  That's the one connected to the gateway (modem).  The other boxes are wireless RECEIVERS that require the WAP.  The WAP is wired to the gateway, not the receivers (hence "wireless").

For clarity, which gateway do you have and what are the models of the wireless boxes?  Any particular reason you want to connect the wireless boxes directly to the gateway?

Hi Skeeterintexas: Thanks for your response. My gateway/modem is a Pace 5268AC FXN. My WAP is a Motorola VAP2500. My Ethernet-connected DVR/receiver is a Motorola VIP2500. My 2 router/WAP-connected DVR receivers are Cisco 1587005.  My goal for attempting to connect with Ethernet cables is to reduce the Wi-Fi RF floating around my house. 

Hello.  The ISB7005s can also operate with an Ethernet connection.  
Kudos on your effort and hope it works out.  You can use a switch to help, but it should support IGMPv3 protocol, also known as Multicast.  

As long as you don't try to mix Internet traffic, especially to a Wireless Access Point or Router, on the same switch as your IPTV, any decently capable Gigabit Ethernet Switch will do fine for your IPTV needs; IGMPv3 peeking is not necessary.

Personally I would not give up the 7005.  
If I have time, I’ll play around with mine to see if I can determine the exact procedure to get the wired connection to activate.   
As long as the 7005 is hardwired to the gateway, there is little risk in causing a firmware reload.  

@JefferMC 

I didn’t suggest using separate switches to segregate the multicast traffic to make the solution as simple as possible, although this is exactly how my setup is, essentially using two ports on the gateway for TV traffic and the rest for standard computer traffic.  

The AT&T standard line is to not mix traffic on a leg from the Gateway.  That's certainly fine, but IMHO unnecessary except in the case of equipment that has issues with multicast.

IGMPv3 support is also unnecessary for a layer 2 switch unless you are trying to support a device that has issues with multicast on the same switch as an IPTV device.  IGMPv3 does not equal multicast.  It is a layer 3 protocol used for initiating distribution of multicast on certain circuits.  A layer 2 device doesn't need to know about subscriptions to properly forward all multicast.  However, it can reduce traffic by "listening in" on the IGMPv3 traffic that it carries and only sending multicast packets whose address has been subscribed to, if it has that feature (known as IGMP peeking).  Technically, it's a violation of the principle of isolation of layers for a layer 2 device to look inside the IP packet data like that.

The flagship device that has issues with multicast is a Wireless Access Point, but there are others. 

I admit to not having understood the needs of Uverse TV.  Here’s a story from several years ago when I was having intermittent problems with my service .
Through a series of calls into tech support, a technician came out to my house and replaced my existing switch with a Netgear one. GS108 IIRC.  problem solved.  A few technicians had made a passing comment about separating traffic which I heard but failed to appreciate because I did not know about the specific protocols used by the service.  Att never published any specific guidance for home network installations that I could find.  
Even to this day, my newer Orbi is unable to properly manage U-verse data correctly, for instance, the time shifting functions won’t work when connected to a satellite.  
What’s the easiest way to help someone venturing into this territory and not create new problems they didn’t already have?   Fortunately no new streaming services work this way and the problem will die when Uverse is finally sunset.  

Great!

Feel free to share your solution.  People do read these threads.  

@JefferMC 

Right, and your post highlights the ability to mix and match equipment, perhaps simply as a function of the RJ-45 connection they all have.  
As a further warning even if a product declares IGMPv3 support, I’ve seen first hand it still fails to support Uverse correctly.  

Yeah, IGMPv3 peeking is not always well implemented.  Which is why I keep qualifying it with "properly implemented."  Some routers that purport to support IPTV may or may not do IGMPv3 at all, but will create VLANs to segregate multicast traffic off only to certain wired ports, keeping it off the Wi-Fi.