I have read that 하오체 is a somewhat archaic style that is heard in historical dramas, but has also become used as an 'Internet style'. I think signs such as '당기시오' and '미시오' are also 하오체.
These seem to be rather disparate usages, if they are indeed all common.
When would the 하오체 style be used? Is there any truth in it being an 'Internet style'? Why is it used on signs?
하오체 is generally perceived "old fashioned" by modern South Korean speakers. Don't know how it's used about North Korea though. Signs are the most prevalent usage nowadays, since it sounds polite and formal.
However, according to http://namu.wiki/, 하오체 was tried as an "Internet speech level", mainly among the Korean community DCinside around 2002. However, it quickly got out of use again after that. So you're right, but it's outdated somewhat.
The Korean language never uses '반말 (non-honorific sentence)' in public signs. For example, the English signs 'Pull' and 'Push' are expressed in 하오체, i.e. '당기시오' and '미시오'. It is just a different cultural phenomenon where honorific expressions are commonly and broadly used. Some signs translate them to '당기세요' and '미세요', and they sound slightly more honorific and friendly than '당기시오' and '미시오'.
'하오체' is rarely used in day-to-day conversation unless you want to sound outdated or make a joke and the following 네이버 국어사전 link on '하오체' confirms it.
<언어> 상대 높임법의 하나. 상대편을 보통으로 높이는 종결형으로, 현대 국어의 구어에서는 거의 쓰지 않는다. ‘빨리 인도로 나오시오.’, ‘왜 꾸물거리시오?’ 따위이다. [비슷한 말] 하오1.
When '하오체' is used by a senior addressing their junior, it sound more like an imperative sentence. For example:
시간이 없어요. 어서 결정하시오. There is no enough time. Make a decision quickly.
It is used when senior feels it awkward to use "어서 결정해라." or "어서 결정해." which sound too non-honorific and impolite as they are used between friends.
