Delta films are said to respond similarly to TMax films. Tri-X, on the other hand, has more severe reciprocity failure with very long exposures. For instance, while a 4 minute exposure becomes 20 minutes with TMax 400, it would become 40 minutes with Tri-X. Similarly, a 10 minute exposure becomes 1 hour with TMax but 2 hours with Tri-X. Pinhole photographer Delio Ansovini has a graph comparing a variety of films
here. Fuji Neopan 100 Acros is a slower film (ISO 100) but apparently suffers from little reciprocity failure for exposures of up to two minutes, then only requires a half stop exposure increase up to about 15 minutes.
Outdoors, with TMax 400, the exposure is usually a second or more, so I haven't had to deal with fractions of seconds, which would be impossible with this camera (with its manually opened and shut aperture). Also, whether the exposure is short or long, any camera movement while opening/shutting the pinhole opening can blur the image (even when a very long exposure is necessary, there are often lamps, candles or other bright objects which will present as lines or wiggles if the camera shakes). My Zero Image does not have an attachment for a cable release (which more expensive models do have) so I always place my palm in front of the pinhole during opening and closing, and remove my hand after the camera is still. Also, I never hand-hold it for any exposure, because even one second this way can result in a blurry mess. I carry a mini-tripod with me, but usually use a table, counter, mailbox, or whatever flat surface is handy to keep the camera still.
Also consider the effect of long exposures on color, if you use color film. The three colors of the film will shift to different degrees with long exposures. I have just been using black and white film, so have not had to deal with this issue.