Ordering a list of elements as shortest euclidean distance between two points

I’ve got a list of points:

figdata = {{67.6769, -1.15057}, {67.9064, -1.30881}, {68.136, -1.01986}, {68.2508, -1.42347}, {68.5951, -1.5152}, {68.7098, -0.946475}, {69.2837, -1.63445}, {69.7428, -1.74453}, {69.9724, -0.905197}, {70.2019, -1.86378}, {70.8905, -0.850158}, {71.0053, -1.96009}, {71.6939, -0.836399}, {72.3826, -2.13438}, {72.6121, -0.822639}, {73.8746, -2.34995}, {73.9894, -0.891437}, {74.4485, -2.4004}, {75.1371, -0.951062}, {75.4815, -2.42792}, {76.1701, -0.987754}, {76.9735, -2.49672}, {77.4326, -1.03362}, {78.236, -2.52423}, {79.0394, -1.10242}, {80.4167, -2.54258}, {80.6462, -1.18039}, {82.2531, -1.26294}, {83.4008, -2.53799}, {84.319, -1.33633}, {85.5815, -1.40054}, {86.9588, -2.54258}, {87.1883, -1.48768}, {88.7951, -1.59317}, {90.0576, -2.54258}, {90.861, -1.67573}, {93.9599, -1.87295}, {92., -2.54258}, {93., -2.54258}, {95.7963, -2.54258}, {98., -2.54258}, {95.911, -1.95551}, {97.2883, -2.04265}, {99.469, -2.18483}, {100.502, -2.25363}, {100.732, -2.5013}, {101.305, -2.46002}, {101.42, -2.32702}, {101.879, -2.40499}} 

I need to plot this data using ListLinePlot so that two neighbouring appear connected with a line. I’ve tried using the following approach:

 Block[{data = figdata, nearel, datanew0 = {}, i = 1},  While[Length[data] > 1,   nearel =     Flatten[Nearest[Delete[data, i], data[[i]],       DistanceFunction -> "EuclideanDistance"]];   datanew0 = Append[datanew0, data[[i]]];   data = Delete[data, i];   i = Position[data, nearel][[1, 1]]   ];  datanew = datanew0  ] 

But, for a reason I don’t know, when I do:

p1 = ListLinePlot[datanew, Frame -> True,     PlotRange -> {{40, 108}, {-2.6, .8}}, AspectRatio -> 1,     FrameStyle -> 15]; p2 = ListPlot[datanew, Frame -> True,     PlotRange -> {{40, 108}, {-2.6, .8}}, AspectRatio -> 1,     FrameStyle -> 15, PlotStyle -> Red]; Show[p1, p2] 

The result i get is:

enter image description here

How would I write a code that solves this problem, and, what is wrong with my piece of code?