Can I get an Ethernet splitter cable to connect a back-up DSL modem to the same router my cable modem is running?

Verizon offered me a discount on my 3-line phone setup (local number, 800 alias number and fax line) if I would add their DSP to one of the three lines. I figured what the heck, if it will save money. I can put DSL on the fax line, which a rarely use. It will be around as a backup if my Comcast cable modem goes down or if Comcast has a service outage. The cable service is 35 megs download, 8 up. So I am not about to switch full time to much slower DSL.

Can I connect both modems to the same Ethernet port on my router, or do I need to physically swap them or use a wireless router for the DSL line? In actual testing with Ping, I’m getting 32.49 Mbps download and 6.07 Mbps upload speed. The only DSL available in my area is max 15 down/ 5 up.