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As you know from my answer to your earlier question, the best preserved tablets containing the standard Akkadian version of the GilgameΕ‘ Epic were discovered in the Library of Ashurbanipal in Nineveh by Hormuzd Rassam in 1853, and are now held in the British Museum.
A number of those tablets are available as high-resolution images from the British Museum website. Note that there is a searchable index to the British Museum's online collection. If you register & request the image you will be sent a high-resolution version by email under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license.
(One of those images - The "Flood tablet" - was attached to my answer to your earlier question. For guidance, the high-resolution .TIF file that I received was 2349 x 2500 pixels)
In general, researchers can generally view the originals by appointment at the museum's study rooms. Photographs may be taken in the study rooms with the permission of study room staff.
Note also that there is specific guidance for Studying cuneiform tablets at the British Museum.