Believe that you are referring to the MidNite Solar KID MPPT Charge Controller.
The KID will need a source of power, ideally, a/some PVs.
Some car batteries may not like an EQ ... have never EQed a Low or No Maintenance car battery. Many/most car batteries are Lead Calcium.
Why do you believe that that battery needs an EQ?
My understanding is the kid has to be used with pv.
It is generally true that it is best to use most MPPT CCs with PV input sources.
Fairly early in the MidNite KID's evolution, it was suggested by MN Engineering, that the KID's Legacy O&P Mode be used with stiff external power sources.
It is now suggested in the KID Manual version 1856, that the U-SET Voc% Input be used for Constant Voltage external sources.
From the 1856 manual, here:http://www.midnitesolar.com/pdfs/kid_manual_rev_1856.pdf
It does state on page 36, to use the U-SET Voc% Input function:
" ... U-SET VOC%
This is a fully manual mode based on a percentage of VOC. The Kid will sweep based on the user set
time in minutes and then park at a user set % of the VOC the Kid found on that sweep. This mode is
useful for testing or constant voltage sources. Press Save then press menu back when done. Modes
will revert to OFF if the up or down arrows are pressed before exiting. ... "
Portions possibly Copyright 2017 MidNite Solar.
We do still use an external SMPS with the KID here. Some safety guidelines when using the KID are, Use an external power supply with an Shout Circuit max current, less than 30 A, a power supply output voltage, not exceeding two times the nominal battery voltage, etc. Just my personal opinions.
FWIW, if the OP has any need of any of the above. Vic