I can find various suggestions about ashigaru, foot soldiers, in combat in Japan and Korea. There are numerous artistic depictions (byobu, folding room screens) and accounts of battle and battle formations. Could someone recommend sources describing ashigaru training and life between campaigns? How did units drill (e.g. close order drill?), unit cohesiveness develop (e.g. recruitment and term of service?) and weapon proficiency improve (e.g. maneuvers and live firing of weapons?) between campaigns? (I am familiar with the Zouhyou Monogatari, the Prof. Turnbull books and Prof. Zaporis' Tour of Duty. Explained skills only imply training and skill development.)
Any suggestions would be welcome. Thank you.
Your best source will be Japanese archives. You should email someone in the Japanese government to request access. Otherwise, I would look for a museum that might hold Japanese or Japanese - English archived materials. Your questions are great, however, you will not be able to get the deep level of detail from many of the secondary sources so far listed. You may also want to look at military professionals from America who were in Japan and left personal accounts. They may get some minor points wrong but you can use that as a strong basis as well.
Ashigaru, literally, light foot 足軽, a foot soldier, used to be called "ji-zamurai 地侍," part farmer, part soldier. The critical period to focus on seems to be the late 16th century, during the time of Toyotomi Hideyoshi 豊臣秀吉, who rose from the peasant "ashigaru" rank to become the unifier of the warring period.
Ashigarus were not really "units" as such but farmers who also served at the time of battles. Just for a quick reading on the Internet, I suggest: http://warfarehistorynetwork.com/daily/military-history/the-japanese-samurai-vs-the-japanese-ashigaru/
The second Internet reading may be: https://www.tofugu.com/japan/ashigaru/
The third item has sources which may be of interest to you: https://www.samurai-archives.com/military.html
If you can read Japanese, you find here that the basic idea of "ashigaru" originated in the Heian period: http://www.weblio.jp/wkpja/content/足軽_足軽の概要
http://warfarehistorynetwork.com/daily/military-history/the-japanese-samurai-vs-the-japanese-ashigaru/
https://www.tofugu.com/japan/ashigaru/
https://www.samurai-archives.com/military.html
http://www.weblio.jp/wkpja/content/足軽_足軽の概要
The Heian period origin of "ashigaru" concept is mentioned in the Heike Monogatari, vol. 4, "Together with about 4,500 ashigaru . . ."; ashigaru is also found during the struggle between the Heike and Minamoto clans, the Gen-Pei Gassen, taking place in the late Heian period, in the 12th century, leading to the establishment of the Kamakura period, the first shogunate to "govern" Japan: 『平家物語』（13世紀成立）巻四に、「足軽共4、500人先立て」とあり、平安末期である源平合戦期にも見られる。