I know that the 5 precepts were intended for lay people. I know that in lay life, most people choose to only keep the 5 precepts, and there is no requirement to keep any more. I know that sometimes lay people take the 8 precepts temporarily. However, is there anything specifically wrong with a lay person keeping the 8 precepts on an ongoing basis? I know it's harder to do as a lay person as opposed to a novice(edit: I meant anagarika). But is it specifically discouraged or wrong for any reason?
In fact, an anagarika (literally a homeless one) would observe the Eight Precepts on a full time basis, but in addition, would not maintain a lay household i.e. they would live a nomadic lifestyle or live in a monastery.
An anagarika is neither a novice monk (samanera) or a fully ordained monk (bhikkhu), but is a kind of informal state between lay life and novice monk, with far less rigid rules compared to monkhood. For e.g. they can deal with money and perform financial transactions. They can also cook their own meals. Monastic rules related to non-intimate interactions with the opposite sex also do not apply to them.
Usually, those who are interested in becoming monks would be asked to spend some time in a monastery, first as an anagarika, then some more time as a novice monk (who keep the Ten Precepts), before undergoing full ordination.
However, there are some people who have preferred to become full time anagarikas like Anagarika Munindra.
Even if one is not an anagarika, it is still foreseeable that a lay person could keep the Eight Precepts on a full time basis.
If your intent is to live a renunciant's life, then yes.
Taking the eight precepts is the best thing you can do to calm the mind.
From personal experience, it is much easier to follow the eight at a monastery. Because of this, you need to be more lenient with beautifying the body (you cannot wear all white all of the time!) and the practice of not eating after noon (just make certain not to eat after your noon meal.)
Anything from which you are running show up on the eight precepts. They are hard, so the practice of the eight precepts must be taken with respect.
You are doing a practice that the noble ones respect.
I would not say "wrong". The precepts encourage awareness that leads to greater skill in practice.
MN8:13.1: Cunda, I say that even giving rise to the thought of skillful qualities is very helpful, let alone following that path in body and speech.
As we study the suttas, we become aware of many other aspects of practice that also apply, such as the brahmaviharas, which are limitless. Love, compassion, rejoicing and equanimity are to be extended and nurtured as an aspect of practice.
For example, I prefer to sleep on futons, but my wife prefers to sleep on high and comfortable beds. She has trouble sleeping and prefers me close, so when she sleeps I sleep by her. When she is not around I sleep wherever.
Another example is that I cook dinner for her but save my portion for eating the next day. Cooking requires tasting, which is eating. When she is away I don't cook in the evening.
Even though my observances are lax, the benefits have proven themselves again and again with greater joy and equanimity. I no longer get "hangry" and can sleep anywhere. I take the Buddha's advice to Cunda to heart.
However, if I were to go forth as a monastic, my behavior would certainly be more strict!