Will an EV-81 tube fit in a Border Patrol DAC?

Sure.  You always want the pin out the same , most important!  And also important is the filament voltage and heater current.   

Look up a Hickok tube sheet for 12ax7.   You will see there are a number of variants, ECC83,7025, CV4004.   12ax7 and 7025 are US designations , ECC is European , CV is a British variant.   

Here's an example of EZ80 and it's cousins.  If you notice there are certain caveats.  I always check the tube data to make sure what is on a sellers page is correct 

https://www.vivatubes.com/6ca4-ez81-6v4-ez80/#:~:text=The%206V4%20and%20EZ80%20are,can%20handle%20higher%20plate%20voltage.