My sound cards always default to the wavetable header for a midi source if there is something plugged in. They only revert to the game port for midi when the wavetable header has nothing in it.

I've never seen any option to switch between the wavetable and the MIDI port on any sound card. I expect the easiest option would be to install a second sound card and configure the MIDI port at a different address. A dedicated midi card that supports intelligent mode, such as the Pico-GUS, could be a good option if you want maximum compatibility.

My experience is that sound cards will simply output MIDI signals to both gameport and wavetable headers. This means that you could get both devices (wavetable and MT-32) triggering at the same time.

To solve this, you need to mute the audio from one or the other. This means either using an external mixer to control sound card and MT-32 audio, or muting the wavetable on the sound card using software.

Some sound cards might have the option to route MIDI signals to wavetable or gameport but not at the same time. This would require using whatever software or driver options for that card to specify routing.

Second that.

I can confirm on both Aztech 3rd gen cards and ESS Solo-1 it works that way; the card just has one MIDI output and both the wavetable header and DA15 port are wired up to it.

There are cards out there with more complex setups, things like the Terratec EWS64 cards have two separate MIDI interfaces - one for the internal GM synth, another for the external port. But that is very exceptional on big, complex cards.

Hi, it's also possible to use two different soundcards (or MPU-401 cards) for MIDI.
Let's say, one is "intelligent" and has an MT-32 synth connected to it, while to other one might be a "dumb" UART type.

MIDI Port 330h.. MT-32
MIDI Port 300h.. GM

Generally speaking, modern DOS games that rely on GM or GS/XG music do use Miles Sound System or any other sound system and can accept an MPU at any i/o port.
Newer MT-32 titles from 1990 up do also support this, I think. Gateway series comes to mind.
It's mainly the older DOS games who expect an intelligent MPU-401 to be at port 330h.

Edit: Snoozer already had essentially mentioned this before.

I run a computer with GS at 332, LA synths at 330, and UART at 300, but I still have to use a mixer for mixing the cards with internal and external sound, like MT-32 which is connected to an LAPC-I.

For my ESS Solo-1, I use a pair of one-line batch files to mute/unmute the wavetable and line in connections as required:

GENMIDI.BAT:

1C:\ESSVOL.EXE /v:15 /l:0 /a:15

MT32.BAT:

1C:\ESSVOL.EXE /v:15 /l:15 /a:0

It ought to be possible to do something similar with any other sound card for which mixer settings can be controlled from the command line. It can also be fun to enable both mixer sources, send Roland's MTGM.SYX to the MT-32 and run it in combination with the wavetable card for extra depth.