In shake table tests in addition to the scale factor of the prototype structure, low cycle fatigue is considered as well (they try to avoid it at first runs!). Based on the what I know, answer to your question is YES,the time history is reduced for a prototype structure, but not 1/6 exactly (they consider shake table capacity + response quantity + low cycle fatigue + ...). Preliminary simulations are used to determine the level of modification factor, and they even change the time axis (compress or decompress) of the acceleration time history. In shake table tests, they often start from low intensity let's say for instance from 0.2x(EQ) => 0.4x(EQ) up to 1.5x(EQ) (for example for sure)or any amplified motion that can bring the bridge close to incipient collapse.
For detailed information on this topic I recommend you read Prof. Saiid Saiidi work at University Nevada, Reno, specifically his former PhD student Ashkan Vosooghi's work. What you asked is not a new topic indeed. It is a shake table test question.
For instance "the ground motion displacement amplitudes
were reduced by 75% to account for the scale of the test model,
which was 0.25." You see the answer to your question!
Below I have included some links to some papers that will help you on this topic. Hope they help. That would be great if you share your research findings here as well, to let us know abut it.
https://nees.unr.edu/Documents/nees/cir ... umn_c1.pdf
https://nees.unr.edu/Documents/nees/Int ... umn_I2.pdf
Arias-Acosta, J. and Sanders, D. (2010) Shake Table Testing of Bridge Columns under Combined Actions. Structures Congress 2010: pp. 1805-1816.
doi: 10.1061/41130(369)165
Saiidi, M. S., Vosooghi, A., Choi, H., & Somerville, P. (2013). Shake Table Studies and Analysis of a Two-Span RC Bridge Model Subjected to a Fault Rupture. Journal of Bridge Engineering.
http://eccomasproceedings.org/cs2013/pdf/1112.pdf
Saiidi, M. S., Vosooghi, A., & Nelson, R. B. (2012). Shake-Table Studies of a Four-Span Reinforced Concrete Bridge. Journal of Structural Engineering, 139(8), 1352-1361.