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The ?g1234 is supposed to be an internal variable that the end user would not see, even in Maxima. See Trac 9825.

But I can't reproduce this in Maxima. Sorry this isn't much of an answer. Maybe this will spur someone one to be able to reproduce it; certainly this is an upstream bug, in the sense that it doesn't raise an error.

Maxima 5.29.1 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) dgl1:'diff('x(t),t,1)=-2*x+2*y+exp(t);
d                         t
(%o1)                     -- (x(t)) = 2 y - 2 x + %e
dt
(%i2) dgl2:'diff('y(t),t,1)=-2*x+3*y+3*exp(t);
d                           t
(%o2)                    -- (y(t)) = 3 y - 2 x + 3 %e
dt
(%i6) atvalue(x(t),t=0,0);
(%o6)                                  0
(%i7) atvalue(y(t),t=0,-1);
(%o7)                                 - 1
(%i8) [desolve([dgl1,dgl2],[x(t),y(t)]);](http://)

desolve: can't handle this case.
-- an error. To debug this try: debugmode(true);