@highfigh was correct above. If the Eico has its own volume and tone section, then you want a fixed line-level output running from the Marantz to the Eico. The Marantz SR7013 has a section on the back labeled "Pre Out" which is normally controlled by the Marantz volume level. You can use the Zone2 or Zone3 from Pre Out but then go into the Marantz settings and set either Zone2 or Zone3 to fixed to get a fixed line-level signal. Use the Tape or Aux input on the Eico.
If you are only using 2 speakers, then just run everything through the Eico. If you have multiple speakers in a surround setup for movies, then things get more complicated. You will either need another pair of speakers dedicated to the Eico, or a good quality speaker switch to switch the two main speakers from the Marantz to the Eico for music. Don't cheap out on the switch. It has to be a 'break before make' switch designed to be used with two amplifiers to avoid damaging your equipment.
Note that you should avoid have the Eico powered on without any speakers connected. Tube amps do not like to be run without a load present.