I do not fly the 767, but the question you posted is pretty general and I remeber my performance analysis for the B-737-800 I used to fly and the differences with the B-747-400 I have the privilige of flying now.
Engine out acceleration altitudes are determined by the operator, FAR 25 states that the minimum altitude to end the second segment is 400 feet AGL thus EICAS warnings inhibits (On aircraft that are equipped with it) will stay that way (inhibited) till passing 400 feet or a preset time so you can concentrate on flying the aicraft on proper speed and path. After those 400 regulation feet, it will depend on the time limit on your aircraft engines (5 or 10 minutes at MAX TO Power) and the paricularities of the airport you are departing from. It is a given that by checking your company's runway analysis tables you are assuring that your takeoff weight on that given day will be such, that you will comply with your second segment climb gradient which as you know, varies from twin to three to four engine aircraft by a set regulation percentage. Furthermore, regulatory agencies want to make sure your departure gradient is at least 2.5% standard or 3.3% if obstacles on the departure path are a factor; if the obstacles are too high or closer, the gradient can be modified accordingly to whatever is required, for example 400 feet per nm equals to 6.67% or a minimum ceiling and visibility is required for the departure so you can see and avoid the obstacle. If you operate out of the US, you will find the required climb gradient of feet per nautical mile published on the different SID for the different runways, to translate that into percentage, just divide it by 60. If you are operating out of ICAO airports it will usualy be in percentage. Now, the performance planners in the airline have to consider if the obstacles are such that a special engine out SID is warranted or not. Some companies will provide you with a table that gives you the climb gradient for different weights and takeoff thrust settings (TO; TO-1 or TO-2) under various OAT temperatures (ISA + 10,15,20,25,30,35), so you can decide if you can continue with the published SID or need to follow the EOSID. but I am getting off track here, back to the engine out acceleration height, most of the operators I know about (Including the current company I work for) use 1000 feet AGL under most conditions for the fleets limited to 5 minutes of TO power and 1500 feet AGL to fleets with 10 minutes TO power. However obstacles do afect these
standard altitudes significantly. For example at max TO power out of SFO on runway 28R, we have an engine out acceleration altitude of 2340 feet and in HKG for runway 7R it is 1340 feet if I remember correctly. This value is published on the same page as the runway analysis performance table. I hope this gives you some additional information to answer your question.
