On and Off neurons
Hartline ("The response of single optic nerve fibers of the vertebrate eye to illumination of the retina", 1935) is the absolute ground zero as far as these neurons are concerned. Hartline was the first to mention On and Off responses to illuminations, and that makes this article worth a very close scrutiny.
The first thing to observe is that it is a "pre-receptive-field" article. He will introduce that concept only a few years later. For now, he is concerned with registering the responses of single optic fibers, but has to abandon the methods Adrian had used for the study of "the simultaneous activity of large numbers of optic fibers", without being able to fall back on those he himself had used for the study of Limulus' vision. Vertebrate neurons are much more densely packed so a new way had to be devised.
He starts with an excised frog eye, and works delicately on the optic fibers to isolate a couple of fibers, and even preferably a single one. "It is not until the bundles have been dissected down until only one, or at most only a few, fibers remain active that a new and striking property of the vertebrate optic response is revealed. For such experiments show conclusively that not all of the optic nerve fibers give the same kind of response to light." (my emphasis)
Please remark the ease with which Hartline mentions the fact that his results are not exclusively based on the study of the responses of a single nerve fiber. He had already mentioned earlier on: "Attempts to obtain single fibers are successful in only a very small percentage of trials". I am not suggesting that Hartline's preparations or his results were faulty, only drawing the attention of the reader to the fact that such an "open mindedness" concerning the number of neurons used for analysis is, in a way, already a precursor of the concept of Receptive Field he will introduce in 1940. He would surely have chosen a different path if he had stuck to the principle of "one receptor one optic fiber" that was the basis of his study of the Limulus. His choice was technically understandable, it was not possible to study single receptors in complex organisms, but the ease with which he forgot this fact remains astounding. Had he been more tuned to the difference in approach, and the consequences of it, he would have certainly been more critical of his own results. I can already say that, long before the formal introduction of receptive fields, his conclusion that there are On and Off neurons, can be understood as a premature application of that future concept. 
The well known results of his experiment were the three types of responses that have become classic paradigms in the science of vision:
- a burst, followed by a steady discharge as long as the stimulation lasts, just like by the Limulus;
- response only to the light being turned on or off (onset and cessation of stimulus);
- and the famous Off response, whereby the fiber only responds to the cessation of illumination.
Hartline was apparently thrilled by the last two reactions. They made the distinction between the responses of the Limulus and the vertebrates very sharp and clear. What should have been a reason to look more critically at the results was taken as the confirmation of what I can only call an intellectual prejudice: the vision of complex animals had to be itself more complex than that of simpler organisms.
The figures he mentions right away would have otherwise certainly made him look twice at the results: "But while Limulus optic nerve fibers invariably show this type of response [the first one], in the frog's retina it is obtained in less than 20 per cent of the fibers." He continues without any hesitation: "At least 50 per cent respond ... with a short burst of impulses at high frequency when the light is turned on, but show no impulses as long as it continues to shine steadily; when the light is turned off there is another brief outburst of impulses."
I cannot help but think that you could not get a better hint that your results were somehow off track. If that were true, that would mean that whenever the light is turned on, our vision is working at half capacity, and remains that way until the light is turned off, allowing the other half to take over!
That does not strike me as very plausible.