My experience with the ADA has been that the bigger the company is the more likely their HR will be prepared for an accommodation request. And the smaller the company is the more likely that any mention of your disability until after they hire you will simply lead to them finding a technical reason not to hire you.
That being said, the ADA allows for you to disclose your condition at any time during an interview process and the employer must provide accommodation.
The strategy that I have taken that has worked well is to bring to the interview a print out from ADA.gov explaining their requirements under the law. This way if you find your self in a situation where accommodation would benefit you you can present it to them and let them decide what to do.
This probably sounds ridiculous but I have seen situations where when presented with a request to halt the interview and provide accommodation the interviewers had heard of neither the ADA or the disability in question.
I'm sorry that this is probably the best recourse there is nothing easy about having a disability its why the ADA exists in the first place. It is unfortunate that many industries specifically Tech tend to treat these disability as the exact kind of qualifier the ADA is designed to protect you from.
Edit based on comments read on OPs original post:
It's really disappointing to see how many comments on OP's post were replied with "be prepared" or simply "know your rights". These arguments quite possible come from a positive place wanting to encourage OP while failing to consider anything real having to do with disability or presenting any real strategies to cope with it.
Many disabilities covered under the ADA can be triggered by extreme moments of mental stress or duress. Epilepsy (as mentioned by OP) and PTSD are both examples of this.
As a person who has worked in the industry for years with one of these conditions I can tell you that the decision to disclose is very complex. I have been through incredibly difficult Technical interviews with zero issue. I have also interviewed at companies where I just didn't have the skills they were looking for even though I had no issues related to my condition in the interview. That being said I have ended up in everything from really hard to really really really entry level silly interviews where something about the tone or the pace or the environment put me in a state where I needed physical help leaving the building.
After tons of interviews in my career I still think it impossible for me to describe what it was that separated the interviews that became episodes from the interviews where I had no problems.
For years when I interviewed at companies where I felt an attack coming on I would simply stop the interview and say:
I appreciate that you took time out of your day to talk to me but I
think that I have reached a point where I'm no longer interested in
the position and I don't want to waste time we could both spend doing
However the further I have progressed in my career the more that I am looking for a particular job rather than looking for A job. This is what has lead to me wanting more and more to seek accommodation. Because there are Jobs that where I know that I have the skills and competency to succeed massively at but where my condition has thrown a silly roadblock in my way.
Edit 2 An example based on reading more comments:
It is difficult for people without disabilities to really internalize the difficulty of actually having that disability. This is especially true when it comes to disabilities of the mind.
That being said these challenges are very real to such a degree that almost every industrialized nation on the planet provides disability related protections to workers.
Additionally in most countries where this accommodations exist it is a crime to claim that you have such a condition when you do not (in the united states it's a felony with a minimum penalty of $10,000 dollars).
Imagine if I was interviewing a candidate for a job who turned out to
be in a wheelchair. Then imagine that as part of their interview
process that candidate was required to climb some stairs. If they
weren't able to climb those stairs we wouldn't be willing to hire
Most rational people would recognize that this would be an insane requirement to put on anyone let alone someone in a wheelchair. Many of the comments to OP's post rotate around haggling with the format.
In our stairs example this is functionally equivalent to saying "well
I'm only asking candidates to climb 1 stair not 12" these types of
half arguments attempt to rationalize a process that may be unfair or
unrealistic no matter how you tune it.
Edit 3 Response to Question
In response to the question about things to suggest:
This is where the ADA printout is very important. It is actually the employers job to suggest alternate activities that would accommodate you. Requesting that they propose several alternate options will give you a list of things that you can pick from that actually accommodate you.
When I need to request accommodation the very first thing I do is request that we take at least a 1 hour break if not that we meet up to discuss a way forward the next day.
The next thing I do is ask them if there has been a previous time where the company interviewed a candidate but didn't use what ever type of exercise you were doing at the time. This is often a good suggestion because companies break their hiring processes all the time for candidates that they really want.
Finally and you shouldn't have to do this but I have found it helps say the following:
I recognize that this isn't an issue that you encounter all the time
and I want you to know that no matter what happens the best legal
outcome is one where both sides of this process believe that they have
had a chance to demonstrate that either I can or can't do this job. I
understand that may mean that you might need to work through several
additional rounds of process with me that you don't go through with
other candidates. However in the end I hope that the additional time
will feel worth it for both of us.