Assemblies of structures such as electronic device assemblies may be connected using light-cured liquid adhesive such as ultraviolet-light-cured adhesive. Light sources such as ultraviolet-light light-emitting diodes may be mounted to a substrate such as a printed circuit board substrate. The substrate may be mounted to an assembly formed from a plurality of structures. The structures may be connected to each other to form an interior cavity within which the substrate and light-emitting diodes are contained. A connector may be included in the assembly. The connector may have input-output pins. Conductive paths may couple the input-output pins to the light-emitting diodes in the cavity. A tool may be used to apply signals to the light-emitting diodes to activate the light-emitting diodes. The light-emitting diodes produce light that cures the adhesive. The light-emitting diodes may be disabled by blowing a fuse after the adhesive has been cured.