You'd have to go into <GMod dir>\gamemodes\terrortown\gamemode\admin.lua and change something in line 108.
By default, it should say something like this:
if (not IsValid(ply)) or ply:IsSuperAdmin() or GetRoundState() != ROUND_ACTIVE then
This might be a ridiculous way of doing it, but it should work fine as long as you have ULib/ULX on the server.
if (not IsValid(ply)) or GetRoundState() != ROUND_ACTIVE or ply:IsUserGroup("Clan Member") or ply:IsUserGroup("Executive") or ply:IsUserGroup("Moderator") or ply:IsAdmin then
That should allow every single group to use the command whether they're dead or not, not sure if inheritance is counted here, and I'm not sure how well "Clan Member" will work, since it has a space in it (I believe I've seen some issues with spaces in group names). At least those groups that are above "admin"/inherit from "admin" should have access anytime.
Although, I'm not sure if this is the right way to do it, to check if someone is alive and allow them to use it if they're dead, you could use this:
if (not IsValid(ply)) or GetRoundState() != ROUND_ACTIVE or ply:IsUserGroup("Clan Member") or ply:IsUserGroup("Executive") or ply:IsUserGroup("Moderator") or ply:IsAdmin or ply:Alive() = "false" then
Then again, I'm not sure if I used "ply:Alive" correct. Some other Lua pro will have to fix that issue if I used it the wrong way.