Eliciting play is to generate interest.
Initiating play means the attention is there or not needed, 'we are going to play now'.
Adult submissive dogs don't generally initiate play with a dominant pack member, they will solicit. There will be a brief moment of solicitation, in which the dominant dog will acknowledge the play behaviours and either ignore the other dog, thereby ending the interaction; or engage. A dog higher in pack order can initiate or elicit play, and is the one who decides when play is over.
But all this is rather academic; and is best see with dogs who have settled rank order. Dominance is not a fixed thing, with immutable rules; each dog has a personal leadership style, based on their personality. Some try to rule with an iron fist (they tend to be less secure individuals, as in humans), some are more permissive leaders, but woe to the pack member who crosses the line!
All of this is less important than your leadership; because the dogs will follow your initiative, and respect the boundries that you put in place. Be aware, tho, that a 1.5 yr old dog might have a little more pack drive than your 8yr old; make sure there is no 'teenager bullying the old man/lady' stuff going on; or inversly, 'cranky old man/lady teaching the whippersnapper a lesson'. If the new dog is more comfortable being top dog, and the older dog is ok with that, or vice versa, then your problems are solved. The problems come when one dog refuses to submit, or the humans decide to elevate (give more perks) the status of a subordinate dog.
But to answer your question lol, the dog that freezes in place and looks 'apprehensive' (actually is telling the other dog 'look how small and still I am, investigate all you want..puppy behaviour). Look at head and tail carriage; frontal, erect posture is a sign of confidence and leadership, but tiptoe and hackles are not. Who walks through doors first, who sits square in front of you for a treat, and who is off to the side (when they are together, dont try this yet), who starts and ends play sessions (the dialogue would go something like this):
Dom dog: hey, lets play!
Sub dog:no I really don't....
Dd: nope sorry, time to play now!
or
sub dog: wanna play? come on, can we?
dom dog: ok, but only for a a second. There is this bush I've been meaning to sniff...or NO..grrrr/blank stare, into the horizon.
Yea, kinda silly. And during play you will see a lot of role reversal, so don't take it into account.
'The Dog's Mind' is a good reference book for this type of stuff. A lot of the material is extrapolated from wolf research, but remember, a dog is not a wolf, any more than a cat is a cheetah. You can have a general idea about what is going on with your dog, but dogs have been separated from wolves for 10,000 years; some behaviours are still there, and some have withered away through breeding selection.
Be aware of your attitude, allow no inter pack aggression, and in a few months, rank will be obvious. To get good at this, study a group of teenagers hanging out. Who is the most insecure? Who is the decision maker? Who is second in command, and how do they relate to those above and below in order (beta groups are the most interesting, and least stable of all groups)? Who is the out cast, or last in the group? Humans are much more complex than dogs, but some of the observations are relevant to both. It is facinating....
Can you tell I have an interest in human and canine societies? yeesh.
This comes from direct observation of my dogs (I have three, loose in the house); I don't have Eds tape, so I can't comment on it.
Relation is reciprocity. How we are educated by children, by animals!-Martin Buber