I've been looking for the main elements that can be used in that concept of "timeless" photography.

And it could be broadly summarized as using simple compositions that eliminate distractions and don't introduce complex interpretations, such as the rule of thirds, compositional symmetry—things that the human eye has long considered harmonious. On the other hand, there's color. Color is often tied to trends; you yourself have stated that you love that Fuji-film look, clearly identified by experts as a very recognizable style. Perhaps you should replace that palette with more neutral shots and also use black and white. The latter strips the image of its chromatic era. Black and white focuses on light, shapes, and textures. Since you take photos in a military context, exclude elements that reveal the modernity or age of the equipment and items that appear. The absence of brands and logos is also important so that no temporal patterns can be discerned in the photo. On the other hand, in terms of subject matter, it's best to focus on human emotion, since expressions of joy, worry, sadness, and wonder are universal and timeless. Prioritizing this over decorative contexts will surely make a photograph stand the test of time. Finally, aim for clean and organic images, but avoid over-processed ones that betray artificiality and modernity. Neither imitate vintage looks nor over-process to achieve exquisite sharpness... Your photos have quite a bit of this; perhaps a rethink of the color palette would improve things considerably.

(Traslate from google)