Wow! The harshness of some of the responses!
I took the OP as not really knowing much about the subject and so (I think) somewhat confusing the concept of a gag strap (which is how I interpreted "suicide strap") and a bungee necklace.
To be clear, a gag strap is used by some CCR divers to hold their "mouthpiece" in their mouth, even if they, for example, pass out. It goes around the back of the head and is pulled tight enough to keep the mouthpiece in and maintain a seal even with an unconscious diver's mouth.
That is somewhat different than a bungee necklace that holds one of your 2nd stage regulators just below your chin/throat.
I have been using the "streamlined open water" (i.e. primary on long hose and secondary on short hose with bungee necklace) since I bought my first reg set right after I completed my OW training. In my opinion, you are best off to buy some bungee cord and make your own bungee necklace (if you want to use that configuration). The ideal arrangement will be that the length of the bungee necklace is just right so that you could get your alternate into your mouth without using your hands if you really needed to. Store bought necklaces are going to be too long for almost anyone to do that, since they are kind of one size fits all.
Also, there seem to be two schools of thought on how to attach the bungee to your 2nd stage.
One way is to use two Fishman knots to make a necklace with an O between the knots that you can put around the mouthpiece and then pull tight (since the knots slide). I used to do it that way. I had more than one occasion of something tugging on my reg and having it pull out of the bungee necklace. Too easily, in my opinion, even though I tried to cinch the necklace down on it as tight as I could.
The second way is to remove the zip tie holding the mouthpiece on, tie a knot in each end of the bungee. A regular overhand knot will do. Then put a new zip tie around the mouthpiece and put the bungee through that on either side. Then tighten the zip tie as much as you can. The bungee can't really pull out, this way. The only way you could pull the 2nd stage out of the "bungee necklace" is if the zip tie broke or the whole mouthpiece assembly came off the reg. This second way is the way I'm doing mine now. This way also makes it easier to get the bungee length just right.
I took the OP as not really knowing much about the subject and so (I think) somewhat confusing the concept of a gag strap (which is how I interpreted "suicide strap") and a bungee necklace.
To be clear, a gag strap is used by some CCR divers to hold their "mouthpiece" in their mouth, even if they, for example, pass out. It goes around the back of the head and is pulled tight enough to keep the mouthpiece in and maintain a seal even with an unconscious diver's mouth.
That is somewhat different than a bungee necklace that holds one of your 2nd stage regulators just below your chin/throat.
I have been using the "streamlined open water" (i.e. primary on long hose and secondary on short hose with bungee necklace) since I bought my first reg set right after I completed my OW training. In my opinion, you are best off to buy some bungee cord and make your own bungee necklace (if you want to use that configuration). The ideal arrangement will be that the length of the bungee necklace is just right so that you could get your alternate into your mouth without using your hands if you really needed to. Store bought necklaces are going to be too long for almost anyone to do that, since they are kind of one size fits all.
Also, there seem to be two schools of thought on how to attach the bungee to your 2nd stage.
One way is to use two Fishman knots to make a necklace with an O between the knots that you can put around the mouthpiece and then pull tight (since the knots slide). I used to do it that way. I had more than one occasion of something tugging on my reg and having it pull out of the bungee necklace. Too easily, in my opinion, even though I tried to cinch the necklace down on it as tight as I could.
The second way is to remove the zip tie holding the mouthpiece on, tie a knot in each end of the bungee. A regular overhand knot will do. Then put a new zip tie around the mouthpiece and put the bungee through that on either side. Then tighten the zip tie as much as you can. The bungee can't really pull out, this way. The only way you could pull the 2nd stage out of the "bungee necklace" is if the zip tie broke or the whole mouthpiece assembly came off the reg. This second way is the way I'm doing mine now. This way also makes it easier to get the bungee length just right.