where i used to work, sounds very much like this. to me it was outdated but you did learn alot by doing it. it was a very small shop, and we took anything industrila like motors, heater controls, timers, power supplies, etc. and we never had schematics and the only complaints were, it dont work. so literally you had to sit there and draw it out to determine what kind of power it used, how much, and sometimes they would send in just the board and you never knew what you were even working on. i worked there 6 weeks and i realized i was in wayyy over my head.
taking a board and drawing a schematic of it to me, was the hardest thing i ever tried to do. the other 2 techs i worked with, both had worked here doing this for about 25 yrs a piece. it was like walking thru the backyard to them. my first electronics place i worked was called tyco. we did RF stuff and it was easy. the mobiles and portables were DC and you had schematics and they would tell us at orientation for new hires, that component level replacement is out, when in doubt, change the board out.
this last place they actually made you do component level replacement. we didnt have spare boards and often times you had to order your parts. 2 yrs of college did NOTHING to prepare me for this and i dont know that it could. alot of the stuff i have learned i think could only have been learned by experience. once i figured out how to hook something up, it would usually take me 4-5 hrs to test, trouble shoot and as long as we had parts replace whatever was wrong. curve tracers are your friend though. i used them to help me locate the path of the circuit. i am glad i no longer have to do that though as it was mentally tough some days. we didnt have any time limits on how long you had to fix something. and there are some days it would take me all day to figure out what was wrong with something. say something had like 10 IC's, and you had to use 10 signal gen's to input signals, that took time to set up and then you had to get the pin outs of those IC's to see if they were any good. that also took google time there lol.
if you do try and map out the schematic, best of luck, and what i learned is use pencil, coz you will make mistakes along the way, and at first try to figure out where everything is eventually going. is there anything going off the board? is there any inputs from connectors on the board? stuff like that.