You don't come across the cross very often, but I do have that exact cross!
I'll start by saying that mine is also a rescue, and it would be impossible for me to differentiate his innate personality traits from those which result from his less than perfect upbringing.
I'll start by saying that he's more terrier than dachshund, personality wise. Ball obsessed, squirrel chasing (but never catching), and digging up mole hills are some favourite past times, along with swimming in the summer. Awful with cats. Likes to socialise with other dogs, but can be intensely territorial - woe betide any dog that tried to come into our home.
Thoroughly aloof with people he doesn't know - even people who want to say hello to him get blanked (he might take a treat, but then he'll ignore them again - he just isn't interested). Absolutely adores "his" people - it's just that he has a small but intense social circle (plus a few regular visitors who he regards as sentient ball throwers). Seeks affection from his nearest and dearest, but equally goes off by himself and is quite happy to be left alone. He's come into contact with young children before (5+) through family, but to be honest I wouldn't want him in a home full time with children who weren't old enough to recognise body language and to let sleeping dogs lie (11/12+ realistically).
Very bright (too bright, sometimes) and readily trainable if you put the time in. Bladder of steel - he never has accidents. Never destroys anything that isn't a dog toy. He's got a list of random things he doesn't like, and barks to make them go away (he evidently doesn't understand correlation vs causation
) but I've learned to live with that, and we avoid his triggers where possible.
He does have high exercise needs - he'll go all day if you let him, but 2 hours a day is pretty necessary if you want him to be a nice dog! He's about 3.5 now, but I've had him for 2 years, and at the beginning anything less than 2-3 hours a day could lead to distinct feelings of regret. On the plus side, he does sleep through the night and most of the day
I love him dearly, but he's not for the faint hearted, and if I'd acquired a dog via a traditional rescue route there's no way they would have given him to me. We make it work though! Of course, the individual dog you're looking at may be totally different in character to mine. Go along, meet the dog and its carers, and make an assessment on the individual - it's the only sensible thing to do with rescues IMHO.